12x^2-8x-11=6

Solution for 12x^2-8x-11=6 equation:

12x^2-8x-11=6

We move all terms to the left:

12x^2-8x-11-(6)=0

We add all the numbers together, and all the variables

12x^2-8x-17=0

a = 12; b = -8; c = -17;
Δ = b2-4ac
Δ = -82-4·12·(-17)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{55}}{2*12}=\frac{8-4\sqrt{55}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{55}}{2*12}=\frac{8+4\sqrt{55}}{24}
$