x^2=18x-59

Solution for x^2=18x-59 equation:

x^2=18x-59

We move all terms to the left:

x^2-(18x-59)=0

We get rid of parentheses

x^2-18x+59=0

a = 1; b = -18; c = +59;
Δ = b2-4ac
Δ = -182-4·1·59
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{22}}{2*1}=\frac{18-2\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{22}}{2*1}=\frac{18+2\sqrt{22}}{2}
$