12x^2-64x-64=0

Solution for 12x^2-64x-64=0 equation:

12x^2-64x-64=0

a = 12; b = -64; c = -64;
Δ = b2-4ac
Δ = -642-4·12·(-64)
Δ = 7168
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:

$\sqrt{\Delta}=\sqrt{7168}=\sqrt{1024*7}=\sqrt{1024}*\sqrt{7}=32\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-32\sqrt{7}}{2*12}=\frac{64-32\sqrt{7}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+32\sqrt{7}}{2*12}=\frac{64+32\sqrt{7}}{24}
$