x^2+120-7x=180

Solution for x^2+120-7x=180 equation:

x^2+120-7x=180

We move all terms to the left:

x^2+120-7x-(180)=0

We add all the numbers together, and all the variables

x^2-7x-60=0

a = 1; b = -7; c = -60;
Δ = b2-4ac
Δ = -72-4·1·(-60)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*1}=\frac{24}{2}
=12
$