8x(x-5)=72

Solution for 8x(x-5)=72 equation:

8x(x-5)=72

We move all terms to the left:

8x(x-5)-(72)=0

We multiply parentheses

8x^2-40x-72=0

a = 8; b = -40; c = -72;
Δ = b2-4ac
Δ = -402-4·8·(-72)
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{61}}{2*8}=\frac{40-8\sqrt{61}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{61}}{2*8}=\frac{40+8\sqrt{61}}{16}
$