X(x+60)=180

Solution for X(x+60)=180 equation:

X(X+60)=180

We move all terms to the left:

X(X+60)-(180)=0

We multiply parentheses

X^2+60X-180=0

a = 1; b = 60; c = -180;
Δ = b2-4ac
Δ = 602-4·1·(-180)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-12\sqrt{30}}{2*1}=\frac{-60-12\sqrt{30}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+12\sqrt{30}}{2*1}=\frac{-60+12\sqrt{30}}{2}
$