6/x=4/3x+1

Solution for 6/x=4/3x+1 equation:

6/x=4/3x+1

We move all terms to the left:

6/x-(4/3x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

6/x-4/3x-1=0

We calculate fractions


18x/3x^2+(-4x)/3x^2-1=0

We multiply all the terms by the denominator


18x+(-4x)-1*3x^2=0

Wy multiply elements

-3x^2+18x+(-4x)=0

We get rid of parentheses

-3x^2+18x-4x=0

We add all the numbers together, and all the variables

-3x^2+14x=0

a = -3; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-3)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-3}=\frac{-28}{-6}
=4+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-3}=\frac{0}{-6}
=0
$