-2x2+2x+11=0

Solution for -2x2+2x+11=0 equation:

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

a = -2; b = 2; c = +11;
Δ = b2-4ac
Δ = 22-4·(-2)·11
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{23}}{2*-2}=\frac{-2-2\sqrt{23}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{23}}{2*-2}=\frac{-2+2\sqrt{23}}{-4}
$