Y=4x^2-6x-12

Solution for Y=4x^2-6x-12 equation:

=4Y^2-6Y-12

We move all terms to the left:

-(4Y^2-6Y-12)=0

We get rid of parentheses

-4Y^2+6Y+12=0

a = -4; b = 6; c = +12;
Δ = b2-4ac
Δ = 62-4·(-4)·12
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{57}}{2*-4}=\frac{-6-2\sqrt{57}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{57}}{2*-4}=\frac{-6+2\sqrt{57}}{-8}
$