6x^2+12x-78=-4

Solution for 6x^2+12x-78=-4 equation:

6x^2+12x-78=-4

We move all terms to the left:

6x^2+12x-78-(-4)=0

We add all the numbers together, and all the variables

6x^2+12x-74=0

a = 6; b = 12; c = -74;
Δ = b2-4ac
Δ = 122-4·6·(-74)
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{30}}{2*6}=\frac{-12-8\sqrt{30}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{30}}{2*6}=\frac{-12+8\sqrt{30}}{12}
$