2x^2=-2x+11

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

2x^2=-2x+11

We move all terms to the left:

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

We get rid of parentheses

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}
$