1/9x+28=2/3x

Solution for 1/9x+28=2/3x equation:

1/9x+28=2/3x

We move all terms to the left:

1/9x+28-(2/3x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/9x-(+2/3x)+28=0

We get rid of parentheses

1/9x-2/3x+28=0

We calculate fractions


3x/27x^2+(-18x)/27x^2+28=0

We multiply all the terms by the denominator


3x+(-18x)+28*27x^2=0

Wy multiply elements

756x^2+3x+(-18x)=0

We get rid of parentheses

756x^2+3x-18x=0

We add all the numbers together, and all the variables

756x^2-15x=0

a = 756; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·756·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*756}=\frac{0}{1512}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*756}=\frac{30}{1512}
=5/252
$