x^2=18x-63

Solution for x^2=18x-63 equation:

x^2=18x-63

We move all terms to the left:

x^2-(18x-63)=0

We get rid of parentheses

x^2-18x+63=0

a = 1; b = -18; c = +63;
Δ = b2-4ac
Δ = -182-4·1·63
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{2}}{2*1}=\frac{18-6\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{2}}{2*1}=\frac{18+6\sqrt{2}}{2}
$