6x2-12x-78=0

Solution for 6x2-12x-78=0 equation:

6x^2-12x-78=0

a = 6; b = -12; c = -78;
Δ = b2-4ac
Δ = -122-4·6·(-78)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{14}}{2*6}=\frac{12-12\sqrt{14}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{14}}{2*6}=\frac{12+12\sqrt{14}}{12}
$