6x^2-28x-22=0

Solution for 6x^2-28x-22=0 equation:

6x^2-28x-22=0

a = 6; b = -28; c = -22;
Δ = b2-4ac
Δ = -282-4·6·(-22)
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{82}}{2*6}=\frac{28-4\sqrt{82}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{82}}{2*6}=\frac{28+4\sqrt{82}}{12}
$