0=2x2+13x-24

Solution for 0=2x2+13x-24 equation:

0=2x^2+13x-24

We move all terms to the left:

0-(2x^2+13x-24)=0

We add all the numbers together, and all the variables

-(2x^2+13x-24)=0

We get rid of parentheses

-2x^2-13x+24=0

a = -2; b = -13; c = +24;
Δ = b2-4ac
Δ = -132-4·(-2)·24
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-19}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+19}{2*-2}=\frac{32}{-4}
=-8
$