Y=-2x2-4x+11

Solution for Y=-2x2-4x+11 equation:

=-2Y^2-4Y+11

We move all terms to the left:

-(-2Y^2-4Y+11)=0

We get rid of parentheses

2Y^2+4Y-11=0

a = 2; b = 4; c = -11;
Δ = b2-4ac
Δ = 42-4·2·(-11)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{26}}{2*2}=\frac{-4-2\sqrt{26}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{26}}{2*2}=\frac{-4+2\sqrt{26}}{4}
$