0=-4x^2-10x+24

Solution for 0=-4x^2-10x+24 equation:

0=-4x^2-10x+24

We move all terms to the left:

0-(-4x^2-10x+24)=0

We add all the numbers together, and all the variables

-(-4x^2-10x+24)=0

We get rid of parentheses

4x^2+10x-24=0

a = 4; b = 10; c = -24;
Δ = b2-4ac
Δ = 102-4·4·(-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{-(10)-22}{2*4}=\frac{-32}{8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+22}{2*4}=\frac{12}{8}
=1+1/2
$