6x^2-14x-9=0

Solution for 6x^2-14x-9=0 equation:

6x^2-14x-9=0

a = 6; b = -14; c = -9;
Δ = b2-4ac
Δ = -142-4·6·(-9)
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{103}}{2*6}=\frac{14-2\sqrt{103}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{103}}{2*6}=\frac{14+2\sqrt{103}}{12}
$