x2-8x=72

Solution for x2-8x=72 equation:

x2-8x=72

We move all terms to the left:

x2-8x-(72)=0

We add all the numbers together, and all the variables

x^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:

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