9x^2-12x-6=0

Solution for 9x^2-12x-6=0 equation:

9x^2-12x-6=0

a = 9; b = -12; c = -6;
Δ = b2-4ac
Δ = -122-4·9·(-6)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{10}}{2*9}=\frac{12-6\sqrt{10}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{10}}{2*9}=\frac{12+6\sqrt{10}}{18}
$