80-15x+x^2=180

Solution for 80-15x+x^2=180 equation:

80-15x+x^2=180

We move all terms to the left:

80-15x+x^2-(180)=0

We add all the numbers together, and all the variables

x^2-15x-100=0

a = 1; b = -15; c = -100;
Δ = b2-4ac
Δ = -152-4·1·(-100)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-25}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+25}{2*1}=\frac{40}{2}
=20
$