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+4x-48

Back to the equation:

-(2x^2+4x-48)


We get rid of parentheses

-2x^2-4x+48+4224=0

We add all the numbers together, and all the variables

-2x^2-4x+4272=0

a = -2; b = -4; c = +4272;
Δ = b2-4ac
Δ = -42-4·(-2)·4272
Δ = 34192
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:

$\sqrt{\Delta}=\sqrt{34192}=\sqrt{16*2137}=\sqrt{16}*\sqrt{2137}=4\sqrt{2137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2137}}{2*-2}=\frac{4-4\sqrt{2137}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2137}}{2*-2}=\frac{4+4\sqrt{2137}}{-4}
$