Question 628977
<pre>    
         x² = 8x - 5

Get 0 on the right:

x² - 8x + 5 = 0

That doesn't factor so we have to use the quadratic formula:

a = 1, b = -8, c = 5

x = {{{(-b +- sqrt( b^2-4*a*c ))/(2*a)}}} 

x = {{{(-(-8) +- sqrt( (-8)^2-4*(1)*(5) ))/(2*(1)) }}} 

x = {{{(8 +- sqrt(64-20 ))/2 }}}

x = {{{(8 +- sqrt(44 ))/2 }}}

x = {{{(8 +- sqrt(4*11 ))/2 }}}

x = {{{(8 +- sqrt(4)sqrt(11 ))/2 }}}

x = {{{(8 +- 2sqrt(11 ))/2 }}}

x = {{{(2(4 +- sqrt(11) ))/2 }}}

x = {{{(cross(2)(4 +- sqrt(11) ))/cross(2) }}}
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x = 4 ± <font face = "symbol">Ö</font>11

Two solutions:
         __              __ 
x = 4 + <font face = "symbol">Ö</font>11 and x = 4 - <font face = "symbol">Ö</font>11

Edwin</pre>