(45)(24)=(2x-8)(x+8)

Solution for (45)(24)=(2x-8)(x+8) equation:

(45)(24)=(2x-8)(x+8)

We move all terms to the left:

(45)(24)-((2x-8)(x+8))=0

We multiply parentheses ..

-((+2x^2+16x-8x-64))+4524=0


We calculate terms in parentheses: -((+2x^2+16x-8x-64)), so:

(+2x^2+16x-8x-64)

We get rid of parentheses

2x^2+16x-8x-64

We add all the numbers together, and all the variables

2x^2+8x-64

Back to the equation:

-(2x^2+8x-64)


We get rid of parentheses

-2x^2-8x+64+4524=0

We add all the numbers together, and all the variables

-2x^2-8x+4588=0

a = -2; b = -8; c = +4588;
Δ = b2-4ac
Δ = -82-4·(-2)·4588
Δ = 36768
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{36768}=\sqrt{16*2298}=\sqrt{16}*\sqrt{2298}=4\sqrt{2298}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{2298}}{2*-2}=\frac{8-4\sqrt{2298}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{2298}}{2*-2}=\frac{8+4\sqrt{2298}}{-4}
$