4(x-6)x=8

Solution for 4(x-6)x=8 equation:

4(x-6)x=8

We move all terms to the left:

4(x-6)x-(8)=0

We multiply parentheses

4x^2-24x-8=0

a = 4; b = -24; c = -8;
Δ = b2-4ac
Δ = -242-4·4·(-8)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{11}}{2*4}=\frac{24-8\sqrt{11}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{11}}{2*4}=\frac{24+8\sqrt{11}}{8}
$