8x+32=x^2+6x

Solution for 8x+32=x^2+6x equation:

8x+32=x^2+6x

We move all terms to the left:

8x+32-(x^2+6x)=0

We get rid of parentheses

-x^2+8x-6x+32=0

We add all the numbers together, and all the variables

-1x^2+2x+32=0

a = -1; b = 2; c = +32;
Δ = b2-4ac
Δ = 22-4·(-1)·32
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{33}}{2*-1}=\frac{-2-2\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{33}}{2*-1}=\frac{-2+2\sqrt{33}}{-2}
$