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 = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{35}}{2*1}=\frac{18-4\sqrt{35}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{35}}{2*1}=\frac{18+4\sqrt{35}}{2}
$