Y=4y^2+4y-6

Solution for Y=4y^2+4y-6 equation:

=4Y^2+4Y-6

We move all terms to the left:

-(4Y^2+4Y-6)=0

We get rid of parentheses

-4Y^2-4Y+6=0

a = -4; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-4)·6
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*-4}=\frac{4-4\sqrt{7}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*-4}=\frac{4+4\sqrt{7}}{-8}
$