(x-1)(x+3)+500=517+x

Solution for (x-1)(x+3)+500=517+x equation:

(x-1)(x+3)+500=517+x

We move all terms to the left:

(x-1)(x+3)+500-(517+x)=0

We add all the numbers together, and all the variables

(x-1)(x+3)-(x+517)+500=0

We get rid of parentheses

(x-1)(x+3)-x-517+500=0

We multiply parentheses ..

(+x^2+3x-1x-3)-x-517+500=0

We add all the numbers together, and all the variables

(+x^2+3x-1x-3)-1x-17=0

We get rid of parentheses

x^2+3x-1x-1x-3-17=0

We add all the numbers together, and all the variables

x^2+x-20=0

a = 1; b = 1; c = -20;
Δ = b2-4ac
Δ = 12-4·1·(-20)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*1}=\frac{8}{2}
=4
$