-2x^2+2x=-25

Solution for -2x^2+2x=-25 equation:

-2x^2+2x=-25

We move all terms to the left:

-2x^2+2x-(-25)=0

We add all the numbers together, and all the variables

-2x^2+2x+25=0

a = -2; b = 2; c = +25;
Δ = b2-4ac
Δ = 22-4·(-2)·25
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{51}}{2*-2}=\frac{-2-2\sqrt{51}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{51}}{2*-2}=\frac{-2+2\sqrt{51}}{-4}
$