2/3x+2=1/9x+7

Solution for 2/3x+2=1/9x+7 equation:

2/3x+2=1/9x+7

We move all terms to the left:

2/3x+2-(1/9x+7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x+7)!=0

x∈R


We get rid of parentheses

2/3x-1/9x-7+2=0

We calculate fractions


18x/27x^2+(-3x)/27x^2-7+2=0

We add all the numbers together, and all the variables

18x/27x^2+(-3x)/27x^2-5=0

We multiply all the terms by the denominator


18x+(-3x)-5*27x^2=0

Wy multiply elements

-135x^2+18x+(-3x)=0

We get rid of parentheses

-135x^2+18x-3x=0

We add all the numbers together, and all the variables

-135x^2+15x=0

a = -135; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-135)·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*-135}=\frac{-30}{-270}
=1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-135}=\frac{0}{-270}
=0
$