(42)(24)=(2x-8)(x-6)

Solution for (42)(24)=(2x-8)(x-6) equation:

(42)(24)=(2x-8)(x-6)

We move all terms to the left:

(42)(24)-((2x-8)(x-6))=0

We multiply parentheses ..

-((+2x^2-12x-8x+48))+4224=0


We calculate terms in parentheses: -((+2x^2-12x-8x+48)), so:

(+2x^2-12x-8x+48)

We get rid of parentheses

2x^2-12x-8x+48

We add all the numbers together, and all the variables

2x^2-20x+48

Back to the equation:

-(2x^2-20x+48)


We get rid of parentheses

-2x^2+20x-48+4224=0

We add all the numbers together, and all the variables

-2x^2+20x+4176=0

a = -2; b = 20; c = +4176;
Δ = b2-4ac
Δ = 202-4·(-2)·4176
Δ = 33808
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:

$\sqrt{\Delta}=\sqrt{33808}=\sqrt{16*2113}=\sqrt{16}*\sqrt{2113}=4\sqrt{2113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{2113}}{2*-2}=\frac{-20-4\sqrt{2113}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{2113}}{2*-2}=\frac{-20+4\sqrt{2113}}{-4}
$