239=-x^2-2x+527

Solution for 239=-x^2-2x+527 equation:

239=-x^2-2x+527

We move all terms to the left:

239-(-x^2-2x+527)=0

We get rid of parentheses

x^2+2x-527+239=0

We add all the numbers together, and all the variables

x^2+2x-288=0

a = 1; b = 2; c = -288;
Δ = b2-4ac
Δ = 22-4·1·(-288)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-34}{2*1}=\frac{-36}{2}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+34}{2*1}=\frac{32}{2}
=16
$