x^2+60x=4500

Solution for x^2+60x=4500 equation:

x^2+60x=4500

We move all terms to the left:

x^2+60x-(4500)=0

a = 1; b = 60; c = -4500;
Δ = b2-4ac
Δ = 602-4·1·(-4500)
Δ = 21600
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:

$\sqrt{\Delta}=\sqrt{21600}=\sqrt{3600*6}=\sqrt{3600}*\sqrt{6}=60\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60\sqrt{6}}{2*1}=\frac{-60-60\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60\sqrt{6}}{2*1}=\frac{-60+60\sqrt{6}}{2}
$