6x=5/8x

Solution for 6x=5/8x equation:

6x=5/8x

We move all terms to the left:

6x-(5/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+5/8x)=0

We get rid of parentheses

6x-5/8x=0

We multiply all the terms by the denominator


6x*8x-5=0

Wy multiply elements

48x^2-5=0

a = 48; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·48·(-5)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*48}=\frac{0-8\sqrt{15}}{96}
=-\frac{8\sqrt{15}}{96}
=-\frac{\sqrt{15}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*48}=\frac{0+8\sqrt{15}}{96}
=\frac{8\sqrt{15}}{96}
=\frac{\sqrt{15}}{12}
$