y^2+3y^2-72=180

Solution for y^2+3y^2-72=180 equation:

y^2+3y^2-72=180

We move all terms to the left:

y^2+3y^2-72-(180)=0

We add all the numbers together, and all the variables

4y^2-252=0

a = 4; b = 0; c = -252;
Δ = b2-4ac
Δ = 02-4·4·(-252)
Δ = 4032
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{7}}{2*4}=\frac{0-24\sqrt{7}}{8}
=-\frac{24\sqrt{7}}{8}
=-3\sqrt{7}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{7}}{2*4}=\frac{0+24\sqrt{7}}{8}
=\frac{24\sqrt{7}}{8}
=3\sqrt{7}
$