X^2-11x+60=180

Solution for X^2-11x+60=180 equation:

X^2-11X+60=180

We move all terms to the left:

X^2-11X+60-(180)=0

We add all the numbers together, and all the variables

X^2-11X-120=0

a = 1; b = -11; c = -120;
Δ = b2-4ac
Δ = -112-4·1·(-120)
Δ = 601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{601}}{2*1}=\frac{11-\sqrt{601}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{601}}{2*1}=\frac{11+\sqrt{601}}{2}
$