12x^2-36x-22=0

Solution for 12x^2-36x-22=0 equation:

12x^2-36x-22=0

a = 12; b = -36; c = -22;
Δ = b2-4ac
Δ = -362-4·12·(-22)
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-28\sqrt{3}}{2*12}=\frac{36-28\sqrt{3}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+28\sqrt{3}}{2*12}=\frac{36+28\sqrt{3}}{24}
$