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<b>let </b><font color="Maroon" title="c1">b</font>, <font color="Maroon" title="c2">c</font>, <font color="Maroon" title="c3">d</font>, <font color="Maroon" title="c4">x</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>







<b>assume </b><a NAME="E1:33"/><i><font color="Green" title="E8">A1</font></i>: 
( <font color="Maroon" title="c1">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 &amp;  <a href="quin_1.html#K1" title="QUIN_1:func.1">delta</a> <font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">c</font>,<font color="Maroon" title="c3">d</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 ;<br/>

<b>assume </b><a NAME="E2:33"/>
 <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> 0,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">c</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/>

<a NAME="E3:33"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">b</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
;<br/>
<a NAME="E4:33"/><b>then </b>
 <a href="polyeq_1.html#K3" title="POLYEQ_1:func.3">Polynom</a> <font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">c</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
;<br/>
<b>hence </b><a NAME="E5:33"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1" title="QUIN_1:func.1">delta</a> <font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">c</font>,<font color="Maroon" title="c3">d</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c1">b</font></span>)</span> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1" title="QUIN_1:func.1">delta</a> <font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">c</font>,<font color="Maroon" title="c3">d</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c1">b</font></span>)</span> )
 <b>by </b><i><a class="txt" href="polyeq_1.html#E1:33"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="polyeq_1.html#T5" target="_self" title="POLYEQ_1:th.5">Th5</a></i>;<br/>


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