8x=24/6x

Solution for 8x=24/6x equation:

8x=24/6x

We move all terms to the left:

8x-(24/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

8x-24/6x=0

We multiply all the terms by the denominator


8x*6x-24=0

Wy multiply elements

48x^2-24=0

a = 48; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·48·(-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{-(0)-48\sqrt{2}}{2*48}=\frac{0-48\sqrt{2}}{96}
=-\frac{48\sqrt{2}}{96}
=-\frac{\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{2}}{2*48}=\frac{0+48\sqrt{2}}{96}
=\frac{48\sqrt{2}}{96}
=\frac{\sqrt{2}}{2}
$