Y=-4x^2+6x+8

Solution for Y=-4x^2+6x+8 equation:

=-4Y^2+6Y+8

We move all terms to the left:

-(-4Y^2+6Y+8)=0

We get rid of parentheses

4Y^2-6Y-8=0

a = 4; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·4·(-8)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{41}}{2*4}=\frac{6-2\sqrt{41}}{8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{41}}{2*4}=\frac{6+2\sqrt{41}}{8}
$