4/x=x/3x-5

Solution for 4/x=x/3x-5 equation:

4/x=x/3x-5

We move all terms to the left:

4/x-(x/3x-5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-5)!=0

x∈R


We get rid of parentheses

4/x-x/3x+5=0

We calculate fractions


(-1x^2)/3x^2+12x/3x^2+5=0

We multiply all the terms by the denominator


(-1x^2)+12x+5*3x^2=0

Wy multiply elements

(-1x^2)+15x^2+12x=0

We get rid of parentheses

-1x^2+15x^2+12x=0

We add all the numbers together, and all the variables

14x^2+12x=0

a = 14; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·14·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*14}=\frac{-24}{28}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*14}=\frac{0}{28}
=0
$