255+x^2=9x*9x

Solution for 255+x^2=9x*9x equation:

255+x^2=9x*9x

We move all terms to the left:

255+x^2-(9x*9x)=0

We add all the numbers together, and all the variables

x^2-(+9x*9x)+255=0

We get rid of parentheses

x^2-9x*9x+255=0

Wy multiply elements

x^2-81x^2+255=0

We add all the numbers together, and all the variables

-80x^2+255=0

a = -80; b = 0; c = +255;
Δ = b2-4ac
Δ = 02-4·(-80)·255
Δ = 81600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{81600}=\sqrt{1600*51}=\sqrt{1600}*\sqrt{51}=40\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{51}}{2*-80}=\frac{0-40\sqrt{51}}{-160}
=-\frac{40\sqrt{51}}{-160}
=-\frac{\sqrt{51}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{51}}{2*-80}=\frac{0+40\sqrt{51}}{-160}
=\frac{40\sqrt{51}}{-160}
=\frac{\sqrt{51}}{-4}
$