6*x^2+32*x-768=0

Solution for 6*x^2+32*x-768=0 equation:

6x^2+32x-768=0

a = 6; b = 32; c = -768;
Δ = b2-4ac
Δ = 322-4·6·(-768)
Δ = 19456
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:

$\sqrt{\Delta}=\sqrt{19456}=\sqrt{1024*19}=\sqrt{1024}*\sqrt{19}=32\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32\sqrt{19}}{2*6}=\frac{-32-32\sqrt{19}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32\sqrt{19}}{2*6}=\frac{-32+32\sqrt{19}}{12}
$