Y=x^2+3x-108

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

=Y^2+3Y-108

We move all terms to the left:

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

We get rid of parentheses

-Y^2-3Y+108=0

We add all the numbers together, and all the variables

-1Y^2-3Y+108=0

a = -1; b = -3; c = +108;
Δ = b2-4ac
Δ = -32-4·(-1)·108
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*-1}=\frac{-18}{-2}
=+9
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*-1}=\frac{24}{-2}
=-12
$