6x^2+14x-6=0

Solution for 6x^2+14x-6=0 equation:

6x^2+14x-6=0

a = 6; b = 14; c = -6;
Δ = b2-4ac
Δ = 142-4·6·(-6)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{85}}{2*6}=\frac{-14-2\sqrt{85}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{85}}{2*6}=\frac{-14+2\sqrt{85}}{12}
$