Y=15+114x-3x^2

Solution for Y=15+114x-3x^2 equation:

=15+114Y-3Y^2

We move all terms to the left:

-(15+114Y-3Y^2)=0

We get rid of parentheses

3Y^2-114Y-15=0

a = 3; b = -114; c = -15;
Δ = b2-4ac
Δ = -1142-4·3·(-15)
Δ = 13176
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:

$\sqrt{\Delta}=\sqrt{13176}=\sqrt{36*366}=\sqrt{36}*\sqrt{366}=6\sqrt{366}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-6\sqrt{366}}{2*3}=\frac{114-6\sqrt{366}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+6\sqrt{366}}{2*3}=\frac{114+6\sqrt{366}}{6}
$