X2+17x+120=180

Solution for X2+17x+120=180 equation:

X2+17X+120=180

We move all terms to the left:

X2+17X+120-(180)=0

We add all the numbers together, and all the variables

X^2+17X-60=0

a = 1; b = 17; c = -60;
Δ = b2-4ac
Δ = 172-4·1·(-60)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-23}{2*1}=\frac{-40}{2}
=-20
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+23}{2*1}=\frac{6}{2}
=3
$