6x(4x-4)=20

Solution for 6x(4x-4)=20 equation:

6x(4x-4)=20

We move all terms to the left:

6x(4x-4)-(20)=0

We multiply parentheses

24x^2-24x-20=0

a = 24; b = -24; c = -20;
Δ = b2-4ac
Δ = -242-4·24·(-20)
Δ = 2496
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:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{39}}{2*24}=\frac{24-8\sqrt{39}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{39}}{2*24}=\frac{24+8\sqrt{39}}{48}
$