24=(2x-9)(x+2)

Solution for 24=(2x-9)(x+2) equation:

24=(2x-9)(x+2)

We move all terms to the left:

24-((2x-9)(x+2))=0

We multiply parentheses ..

-((+2x^2+4x-9x-18))+24=0


We calculate terms in parentheses: -((+2x^2+4x-9x-18)), so:

(+2x^2+4x-9x-18)

We get rid of parentheses

2x^2+4x-9x-18

We add all the numbers together, and all the variables

2x^2-5x-18

Back to the equation:

-(2x^2-5x-18)


We get rid of parentheses

-2x^2+5x+18+24=0

We add all the numbers together, and all the variables

-2x^2+5x+42=0

a = -2; b = 5; c = +42;
Δ = b2-4ac
Δ = 52-4·(-2)·42
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{-(5)-19}{2*-2}=\frac{-24}{-4}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*-2}=\frac{14}{-4}
=-3+1/2
$