Y=-3x^2-4x+108

Solution for Y=-3x^2-4x+108 equation:

=-3Y^2-4Y+108

We move all terms to the left:

-(-3Y^2-4Y+108)=0

We get rid of parentheses

3Y^2+4Y-108=0

a = 3; b = 4; c = -108;
Δ = b2-4ac
Δ = 42-4·3·(-108)
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{82}}{2*3}=\frac{-4-4\sqrt{82}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{82}}{2*3}=\frac{-4+4\sqrt{82}}{6}
$