x+500=x2-200

Solution for x+500=x2-200 equation:

x+500=x2-200

We move all terms to the left:

x+500-(x2-200)=0

We add all the numbers together, and all the variables

-(+x^2-200)+x+500=0

We get rid of parentheses

-x^2+x+200+500=0

We add all the numbers together, and all the variables

-1x^2+x+700=0

a = -1; b = 1; c = +700;
Δ = b2-4ac
Δ = 12-4·(-1)·700
Δ = 2801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{2801}}{2*-1}=\frac{-1-\sqrt{2801}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2801}}{2*-1}=\frac{-1+\sqrt{2801}}{-2}
$