0=3x^2+14x-24

Solution for 0=3x^2+14x-24 equation:

0=3x^2+14x-24

We move all terms to the left:

0-(3x^2+14x-24)=0

We add all the numbers together, and all the variables

-(3x^2+14x-24)=0

We get rid of parentheses

-3x^2-14x+24=0

a = -3; b = -14; c = +24;
Δ = b2-4ac
Δ = -142-4·(-3)·24
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-22}{2*-3}=\frac{-8}{-6}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+22}{2*-3}=\frac{36}{-6}
=-6
$