6x^2-4x-222=0

Solution for 6x^2-4x-222=0 equation:

6x^2-4x-222=0

a = 6; b = -4; c = -222;
Δ = b2-4ac
Δ = -42-4·6·(-222)
Δ = 5344
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:

$\sqrt{\Delta}=\sqrt{5344}=\sqrt{16*334}=\sqrt{16}*\sqrt{334}=4\sqrt{334}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{334}}{2*6}=\frac{4-4\sqrt{334}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{334}}{2*6}=\frac{4+4\sqrt{334}}{12}
$