24=6x(8+4x)

Solution for 24=6x(8+4x) equation:

24=6x(8+4x)

We move all terms to the left:

24-(6x(8+4x))=0

We add all the numbers together, and all the variables

-(6x(4x+8))+24=0


We calculate terms in parentheses: -(6x(4x+8)), so:

6x(4x+8)

We multiply parentheses

24x^2+48x

Back to the equation:

-(24x^2+48x)


We get rid of parentheses

-24x^2-48x+24=0

a = -24; b = -48; c = +24;
Δ = b2-4ac
Δ = -482-4·(-24)·24
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48\sqrt{2}}{2*-24}=\frac{48-48\sqrt{2}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48\sqrt{2}}{2*-24}=\frac{48+48\sqrt{2}}{-48}
$