6x^2-24x-11=0

Solution for 6x^2-24x-11=0 equation:

6x^2-24x-11=0

a = 6; b = -24; c = -11;
Δ = b2-4ac
Δ = -242-4·6·(-11)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{210}}{2*6}=\frac{24-2\sqrt{210}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{210}}{2*6}=\frac{24+2\sqrt{210}}{12}
$