4(6/5x)=2/x

Solution for 4(6/5x)=2/x equation:

4(6/5x)=2/x

We move all terms to the left:

4(6/5x)-(2/x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4(+6/5x)-(+2/x)=0

We multiply parentheses

24x-(+2/x)=0

We get rid of parentheses

24x-2/x=0

We multiply all the terms by the denominator


24x*x-2=0

Wy multiply elements

24x^2-2=0

a = 24; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·24·(-2)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*24}=\frac{0-8\sqrt{3}}{48}
=-\frac{8\sqrt{3}}{48}
=-\frac{\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*24}=\frac{0+8\sqrt{3}}{48}
=\frac{8\sqrt{3}}{48}
=\frac{\sqrt{3}}{6}
$