(-2x^2)+8x+11=0

Solution for (-2x^2)+8x+11=0 equation:

(-2x^2)+8x+11=0

We get rid of parentheses

-2x^2+8x+11=0

a = -2; b = 8; c = +11;
Δ = b2-4ac
Δ = 82-4·(-2)·11
Δ = 152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{38}}{2*-2}=\frac{-8-2\sqrt{38}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{38}}{2*-2}=\frac{-8+2\sqrt{38}}{-4}
$