2/x=4/9x+4

Solution for 2/x=4/9x+4 equation:

2/x=4/9x+4

We move all terms to the left:

2/x-(4/9x+4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 9x+4)!=0

x∈R


We get rid of parentheses

2/x-4/9x-4=0

We calculate fractions


18x/9x^2+(-4x)/9x^2-4=0

We multiply all the terms by the denominator


18x+(-4x)-4*9x^2=0

Wy multiply elements

-36x^2+18x+(-4x)=0

We get rid of parentheses

-36x^2+18x-4x=0

We add all the numbers together, and all the variables

-36x^2+14x=0

a = -36; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-36)·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*-36}=\frac{-28}{-72}
=7/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-36}=\frac{0}{-72}
=0
$