12x+36=8x+x^2

Solution for 12x+36=8x+x^2 equation:

12x+36=8x+x^2

We move all terms to the left:

12x+36-(8x+x^2)=0

We get rid of parentheses

-x^2-8x+12x+36=0

We add all the numbers together, and all the variables

-1x^2+4x+36=0

a = -1; b = 4; c = +36;
Δ = b2-4ac
Δ = 42-4·(-1)·36
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{10}}{2*-1}=\frac{-4-4\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{10}}{2*-1}=\frac{-4+4\sqrt{10}}{-2}
$