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 = 7825
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7825}=\sqrt{25*313}=\sqrt{25}*\sqrt{313}=5\sqrt{313}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-5\sqrt{313}}{2*5}=\frac{-65-5\sqrt{313}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+5\sqrt{313}}{2*5}=\frac{-65+5\sqrt{313}}{10}
$