6x^2-12x-93=-5

Solution for 6x^2-12x-93=-5 equation:

6x^2-12x-93=-5

We move all terms to the left:

6x^2-12x-93-(-5)=0

We add all the numbers together, and all the variables

6x^2-12x-88=0

a = 6; b = -12; c = -88;
Δ = b2-4ac
Δ = -122-4·6·(-88)
Δ = 2256
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:

$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{141}}{2*6}=\frac{12-4\sqrt{141}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{141}}{2*6}=\frac{12+4\sqrt{141}}{12}
$