-5a^2+65a=180

Solution for -5a^2+65a=180 equation:

-5a^2+65a=180

We move all terms to the left:

-5a^2+65a-(180)=0

a = -5; b = 65; c = -180;
Δ = b2-4ac
Δ = 652-4·(-5)·(-180)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-25}{2*-5}=\frac{-90}{-10}
=+9
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+25}{2*-5}=\frac{-40}{-10}
=+4
$