6x^2-12x-48=60

Solution for 6x^2-12x-48=60 equation:

6x^2-12x-48=60

We move all terms to the left:

6x^2-12x-48-(60)=0

We add all the numbers together, and all the variables

6x^2-12x-108=0

a = 6; b = -12; c = -108;
Δ = b2-4ac
Δ = -122-4·6·(-108)
Δ = 2736
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:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{19}}{2*6}=\frac{12-12\sqrt{19}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{19}}{2*6}=\frac{12+12\sqrt{19}}{12}
$