1/9x=x/4x

Solution for 1/9x=x/4x equation:

1/9x=x/4x

We move all terms to the left:

1/9x-(x/4x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/9x-(+x/4x)=0

We get rid of parentheses

1/9x-x/4x=0

We calculate fractions


(-9x^2)/36x^2+4x/36x^2=0

We multiply all the terms by the denominator


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

We get rid of parentheses

-9x^2+4x=0

a = -9; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-9)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-9}=\frac{-8}{-18}
=4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-9}=\frac{0}{-18}
=0
$