6x^2-2x-22=0

Solution for 6x^2-2x-22=0 equation:

6x^2-2x-22=0

a = 6; b = -2; c = -22;
Δ = b2-4ac
Δ = -22-4·6·(-22)
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{133}}{2*6}=\frac{2-2\sqrt{133}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{133}}{2*6}=\frac{2+2\sqrt{133}}{12}
$