X+8=x^2+3x-7

Solution for X+8=x^2+3x-7 equation:

X+8=X^2+3X-7

We move all terms to the left:

X+8-(X^2+3X-7)=0

We get rid of parentheses

-X^2+X-3X+7+8=0

We add all the numbers together, and all the variables

-1X^2-2X+15=0

a = -1; b = -2; c = +15;
Δ = b2-4ac
Δ = -22-4·(-1)·15
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*-1}=\frac{-6}{-2}
=+3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*-1}=\frac{10}{-2}
=-5
$