0=4x^2-33x-24

Solution for 0=4x^2-33x-24 equation:

0=4x^2-33x-24

We move all terms to the left:

0-(4x^2-33x-24)=0

We add all the numbers together, and all the variables

-(4x^2-33x-24)=0

We get rid of parentheses

-4x^2+33x+24=0

a = -4; b = 33; c = +24;
Δ = b2-4ac
Δ = 332-4·(-4)·24
Δ = 1473
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{1473}}{2*-4}=\frac{-33-\sqrt{1473}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1473}}{2*-4}=\frac{-33+\sqrt{1473}}{-8}
$