Y=4x2+16x+12

Solution for Y=4x2+16x+12 equation:

=4Y^2+16Y+12

We move all terms to the left:

-(4Y^2+16Y+12)=0

We get rid of parentheses

-4Y^2-16Y-12=0

a = -4; b = -16; c = -12;
Δ = b2-4ac
Δ = -162-4·(-4)·(-12)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8}{2*-4}=\frac{8}{-8}
=-1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*-4}=\frac{24}{-8}
=-3
$