2/x=11/3x-4

Solution for 2/x=11/3x-4 equation:

2/x=11/3x-4

We move all terms to the left:

2/x-(11/3x-4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

2/x-11/3x+4=0

We calculate fractions


6x/3x^2+(-11x)/3x^2+4=0

We multiply all the terms by the denominator


6x+(-11x)+4*3x^2=0

Wy multiply elements

12x^2+6x+(-11x)=0

We get rid of parentheses

12x^2+6x-11x=0

We add all the numbers together, and all the variables

12x^2-5x=0

a = 12; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·12·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*12}=\frac{10}{24}
=5/12
$