8x(2x-6)=128

Solution for 8x(2x-6)=128 equation:

8x(2x-6)=128

We move all terms to the left:

8x(2x-6)-(128)=0

We multiply parentheses

16x^2-48x-128=0

a = 16; b = -48; c = -128;
Δ = b2-4ac
Δ = -482-4·16·(-128)
Δ = 10496
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:

$\sqrt{\Delta}=\sqrt{10496}=\sqrt{256*41}=\sqrt{256}*\sqrt{41}=16\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-16\sqrt{41}}{2*16}=\frac{48-16\sqrt{41}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+16\sqrt{41}}{2*16}=\frac{48+16\sqrt{41}}{32}
$