8x(x-5)=64

Solution for 8x(x-5)=64 equation:

8x(x-5)=64

We move all terms to the left:

8x(x-5)-(64)=0

We multiply parentheses

8x^2-40x-64=0

a = 8; b = -40; c = -64;
Δ = b2-4ac
Δ = -402-4·8·(-64)
Δ = 3648
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:

$\sqrt{\Delta}=\sqrt{3648}=\sqrt{64*57}=\sqrt{64}*\sqrt{57}=8\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{57}}{2*8}=\frac{40-8\sqrt{57}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{57}}{2*8}=\frac{40+8\sqrt{57}}{16}
$