3x^2-12x-116=0

Solution for 3x^2-12x-116=0 equation:

3x^2-12x-116=0

a = 3; b = -12; c = -116;
Δ = b2-4ac
Δ = -122-4·3·(-116)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-16\sqrt{6}}{2*3}=\frac{12-16\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+16\sqrt{6}}{2*3}=\frac{12+16\sqrt{6}}{6}
$