285=-x^2-2x+509

Solution for 285=-x^2-2x+509 equation:

285=-x^2-2x+509

We move all terms to the left:

285-(-x^2-2x+509)=0

We get rid of parentheses

x^2+2x-509+285=0

We add all the numbers together, and all the variables

x^2+2x-224=0

a = 1; b = 2; c = -224;
Δ = b2-4ac
Δ = 22-4·1·(-224)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-30}{2*1}=\frac{-32}{2}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+30}{2*1}=\frac{28}{2}
=14
$