4/3x+3=10/9x+1

Solution for 4/3x+3=10/9x+1 equation:

4/3x+3=10/9x+1

We move all terms to the left:

4/3x+3-(10/9x+1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x+1)!=0

x∈R


We get rid of parentheses

4/3x-10/9x-1+3=0

We calculate fractions


36x/27x^2+(-30x)/27x^2-1+3=0

We add all the numbers together, and all the variables

36x/27x^2+(-30x)/27x^2+2=0

We multiply all the terms by the denominator


36x+(-30x)+2*27x^2=0

Wy multiply elements

54x^2+36x+(-30x)=0

We get rid of parentheses

54x^2+36x-30x=0

We add all the numbers together, and all the variables

54x^2+6x=0

a = 54; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·54·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*54}=\frac{-12}{108}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*54}=\frac{0}{108}
=0
$