Y=-2x^2+10x+11

Solution for Y=-2x^2+10x+11 equation:

=-2Y^2+10Y+11

We move all terms to the left:

-(-2Y^2+10Y+11)=0

We get rid of parentheses

2Y^2-10Y-11=0

a = 2; b = -10; c = -11;
Δ = b2-4ac
Δ = -102-4·2·(-11)
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{47}}{2*2}=\frac{10-2\sqrt{47}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{47}}{2*2}=\frac{10+2\sqrt{47}}{4}
$