72+8x=x*x

Solution for 72+8x=x*x equation:

72+8x=x*x

We move all terms to the left:

72+8x-(x*x)=0

We add all the numbers together, and all the variables

8x-(+x*x)+72=0

We get rid of parentheses

8x-x*x+72=0

Wy multiply elements

-1x^2+8x+72=0

a = -1; b = 8; c = +72;
Δ = b2-4ac
Δ = 82-4·(-1)·72
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{22}}{2*-1}=\frac{-8-4\sqrt{22}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{22}}{2*-1}=\frac{-8+4\sqrt{22}}{-2}
$