Y=-5x^2+8x+4

Solution for Y=-5x^2+8x+4 equation:

=-5Y^2+8Y+4

We move all terms to the left:

-(-5Y^2+8Y+4)=0

We get rid of parentheses

5Y^2-8Y-4=0

a = 5; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·5·(-4)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*5}=\frac{-4}{10}
=-2/5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*5}=\frac{20}{10}
=2
$