4a^2+8a=180

Solution for 4a^2+8a=180 equation:

4a^2+8a=180

We move all terms to the left:

4a^2+8a-(180)=0

a = 4; b = 8; c = -180;
Δ = b2-4ac
Δ = 82-4·4·(-180)
Δ = 2944
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:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{46}}{2*4}=\frac{-8-8\sqrt{46}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{46}}{2*4}=\frac{-8+8\sqrt{46}}{8}
$