Y=3x^2+2x-6

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

=3Y^2+2Y-6

We move all terms to the left:

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

We get rid of parentheses

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

a = -3; b = -2; c = +6;
Δ = b2-4ac
Δ = -22-4·(-3)·6
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*-3}=\frac{2-2\sqrt{19}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*-3}=\frac{2+2\sqrt{19}}{-6}
$