3y^2-48y=-180

Solution for 3y^2-48y=-180 equation:

3y^2-48y=-180

We move all terms to the left:

3y^2-48y-(-180)=0

We add all the numbers together, and all the variables

3y^2-48y+180=0

a = 3; b = -48; c = +180;
Δ = b2-4ac
Δ = -482-4·3·180
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12}{2*3}=\frac{36}{6}
=6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12}{2*3}=\frac{60}{6}
=10
$