Y=3x^2+15x-6

Solution for Y=3x^2+15x-6 equation:

=3Y^2+15Y-6

We move all terms to the left:

-(3Y^2+15Y-6)=0

We get rid of parentheses

-3Y^2-15Y+6=0

a = -3; b = -15; c = +6;
Δ = b2-4ac
Δ = -152-4·(-3)·6
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{33}}{2*-3}=\frac{15-3\sqrt{33}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{33}}{2*-3}=\frac{15+3\sqrt{33}}{-6}
$