0=6x^2-18x-24

Solution for 0=6x^2-18x-24 equation:

0=6x^2-18x-24

We move all terms to the left:

0-(6x^2-18x-24)=0

We add all the numbers together, and all the variables

-(6x^2-18x-24)=0

We get rid of parentheses

-6x^2+18x+24=0

a = -6; b = 18; c = +24;
Δ = b2-4ac
Δ = 182-4·(-6)·24
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-30}{2*-6}=\frac{-48}{-12}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+30}{2*-6}=\frac{12}{-12}
=-1
$