6x^2-24x-9=0

Solution for 6x^2-24x-9=0 equation:

6x^2-24x-9=0

a = 6; b = -24; c = -9;
Δ = b2-4ac
Δ = -242-4·6·(-9)
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{22}}{2*6}=\frac{24-6\sqrt{22}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{22}}{2*6}=\frac{24+6\sqrt{22}}{12}
$