x^2+63*x=180

Solution for x^2+63*x=180 equation:

x^2+63x=180

We move all terms to the left:

x^2+63x-(180)=0

a = 1; b = 63; c = -180;
Δ = b2-4ac
Δ = 632-4·1·(-180)
Δ = 4689
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:

$\sqrt{\Delta}=\sqrt{4689}=\sqrt{9*521}=\sqrt{9}*\sqrt{521}=3\sqrt{521}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{521}}{2*1}=\frac{-63-3\sqrt{521}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{521}}{2*1}=\frac{-63+3\sqrt{521}}{2}
$