x^2-60x=-450

Solution for x^2-60x=-450 equation:

x^2-60x=-450

We move all terms to the left:

x^2-60x-(-450)=0

We add all the numbers together, and all the variables

x^2-60x+450=0

a = 1; b = -60; c = +450;
Δ = b2-4ac
Δ = -602-4·1·450
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-30\sqrt{2}}{2*1}=\frac{60-30\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+30\sqrt{2}}{2*1}=\frac{60+30\sqrt{2}}{2}
$