8x(x-2)=32

Solution for 8x(x-2)=32 equation:

8x(x-2)=32

We move all terms to the left:

8x(x-2)-(32)=0

We multiply parentheses

8x^2-16x-32=0

a = 8; b = -16; c = -32;
Δ = b2-4ac
Δ = -162-4·8·(-32)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16\sqrt{5}}{2*8}=\frac{16-16\sqrt{5}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16\sqrt{5}}{2*8}=\frac{16+16\sqrt{5}}{16}
$