12x^2-1-8x=0

Solution for 12x^2-1-8x=0 equation:

12x^2-1-8x=0

a = 12; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·12·(-1)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*12}=\frac{8-4\sqrt{7}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*12}=\frac{8+4\sqrt{7}}{24}
$