Y=5+15x-3x^2

Solution for Y=5+15x-3x^2 equation:

=5+15Y-3Y^2

We move all terms to the left:

-(5+15Y-3Y^2)=0

We get rid of parentheses

3Y^2-15Y-5=0

a = 3; b = -15; c = -5;
Δ = b2-4ac
Δ = -152-4·3·(-5)
Δ = 285
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{285}}{2*3}=\frac{15-\sqrt{285}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{285}}{2*3}=\frac{15+\sqrt{285}}{6}
$