Y=4x2+8x-20

Solution for Y=4x2+8x-20 equation:

=4Y^2+8Y-20

We move all terms to the left:

-(4Y^2+8Y-20)=0

We get rid of parentheses

-4Y^2-8Y+20=0

a = -4; b = -8; c = +20;
Δ = b2-4ac
Δ = -82-4·(-4)·20
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{6}}{2*-4}=\frac{8-8\sqrt{6}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{6}}{2*-4}=\frac{8+8\sqrt{6}}{-8}
$