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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(x+2)(2x-9)-576=0

We multiply parentheses ..

(+2x^2-9x+4x-18)-576=0

We get rid of parentheses

2x^2-9x+4x-18-576=0

We add all the numbers together, and all the variables

2x^2-5x-594=0

a = 2; b = -5; c = -594;
Δ = b2-4ac
Δ = -52-4·2·(-594)
Δ = 4777
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{-(-5)-\sqrt{4777}}{2*2}=\frac{5-\sqrt{4777}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{4777}}{2*2}=\frac{5+\sqrt{4777}}{4}
$