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

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

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

We move all terms to the left:

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

determiningTheFunctionDomain
(x+6)(2x-8)-4224=0

We multiply parentheses ..

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

We get rid of parentheses

2x^2-8x+12x-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}
$