2/3x+5=-29/9x-2

Solution for 2/3x+5=-29/9x-2 equation:

2/3x+5=-29/9x-2

We move all terms to the left:

2/3x+5-(-29/9x-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x-2)!=0

x∈R


We get rid of parentheses

2/3x+29/9x+2+5=0

We calculate fractions


18x/27x^2+87x/27x^2+2+5=0

We add all the numbers together, and all the variables

18x/27x^2+87x/27x^2+7=0

We multiply all the terms by the denominator


18x+87x+7*27x^2=0

We add all the numbers together, and all the variables

105x+7*27x^2=0

Wy multiply elements

189x^2+105x=0

a = 189; b = 105; c = 0;
Δ = b2-4ac
Δ = 1052-4·189·0
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-105}{2*189}=\frac{-210}{378}
=-5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+105}{2*189}=\frac{0}{378}
=0
$