6x^2+12x-14=138

Solution for 6x^2+12x-14=138 equation:

6x^2+12x-14=138

We move all terms to the left:

6x^2+12x-14-(138)=0

We add all the numbers together, and all the variables

6x^2+12x-152=0

a = 6; b = 12; c = -152;
Δ = b2-4ac
Δ = 122-4·6·(-152)
Δ = 3792
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:

$\sqrt{\Delta}=\sqrt{3792}=\sqrt{16*237}=\sqrt{16}*\sqrt{237}=4\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{237}}{2*6}=\frac{-12-4\sqrt{237}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{237}}{2*6}=\frac{-12+4\sqrt{237}}{12}
$