0=24x^2-6x-111

Solution for 0=24x^2-6x-111 equation:

0=24x^2-6x-111

We move all terms to the left:

0-(24x^2-6x-111)=0

We add all the numbers together, and all the variables

-(24x^2-6x-111)=0

We get rid of parentheses

-24x^2+6x+111=0

a = -24; b = 6; c = +111;
Δ = b2-4ac
Δ = 62-4·(-24)·111
Δ = 10692
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:

$\sqrt{\Delta}=\sqrt{10692}=\sqrt{324*33}=\sqrt{324}*\sqrt{33}=18\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18\sqrt{33}}{2*-24}=\frac{-6-18\sqrt{33}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18\sqrt{33}}{2*-24}=\frac{-6+18\sqrt{33}}{-48}
$