Y=-5x^2-2x+10

Solution for Y=-5x^2-2x+10 equation:

=-5Y^2-2Y+10

We move all terms to the left:

-(-5Y^2-2Y+10)=0

We get rid of parentheses

5Y^2+2Y-10=0

a = 5; b = 2; c = -10;
Δ = b2-4ac
Δ = 22-4·5·(-10)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{51}}{2*5}=\frac{-2-2\sqrt{51}}{10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{51}}{2*5}=\frac{-2+2\sqrt{51}}{10}
$