Y=-10x^2-10x+8

Solution for Y=-10x^2-10x+8 equation:

=-10Y^2-10Y+8

We move all terms to the left:

-(-10Y^2-10Y+8)=0

We get rid of parentheses

10Y^2+10Y-8=0

a = 10; b = 10; c = -8;
Δ = b2-4ac
Δ = 102-4·10·(-8)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{105}}{2*10}=\frac{-10-2\sqrt{105}}{20}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{105}}{2*10}=\frac{-10+2\sqrt{105}}{20}
$