x^2=18x+56=0

Solution for x^2=18x+56=0 equation:

x^2=18x+56=0

We move all terms to the left:

x^2-(18x+56)=0

We get rid of parentheses

x^2-18x-56=0

a = 1; b = -18; c = -56;
Δ = b2-4ac
Δ = -182-4·1·(-56)
Δ = 548
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:

$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{137}}{2*1}=\frac{18-2\sqrt{137}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{137}}{2*1}=\frac{18+2\sqrt{137}}{2}
$