Y=-5x^2-50x+8

Solution for Y=-5x^2-50x+8 equation:

=-5Y^2-50Y+8

We move all terms to the left:

-(-5Y^2-50Y+8)=0

We get rid of parentheses

5Y^2+50Y-8=0

a = 5; b = 50; c = -8;
Δ = b2-4ac
Δ = 502-4·5·(-8)
Δ = 2660
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:

$\sqrt{\Delta}=\sqrt{2660}=\sqrt{4*665}=\sqrt{4}*\sqrt{665}=2\sqrt{665}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{665}}{2*5}=\frac{-50-2\sqrt{665}}{10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{665}}{2*5}=\frac{-50+2\sqrt{665}}{10}
$