4a^2=180

Solution for 4a^2=180 equation:

4a^2=180

We move all terms to the left:

4a^2-(180)=0

a = 4; b = 0; c = -180;
Δ = b2-4ac
Δ = 02-4·4·(-180)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{5}}{2*4}=\frac{0-24\sqrt{5}}{8}
=-\frac{24\sqrt{5}}{8}
=-3\sqrt{5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{5}}{2*4}=\frac{0+24\sqrt{5}}{8}
=\frac{24\sqrt{5}}{8}
=3\sqrt{5}
$