-2/9x+9/5=-5-6/5x

Solution for -2/9x+9/5=-5-6/5x equation:

-2/9x+9/5=-5-6/5x

We move all terms to the left:

-2/9x+9/5-(-5-6/5x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-2/9x-(-6/5x-5)+9/5=0

We get rid of parentheses

-2/9x+6/5x+5+9/5=0

We calculate fractions


(-250x)/1125x^2+54x/1125x^2+81x/1125x^2+5=0

We multiply all the terms by the denominator


(-250x)+54x+81x+5*1125x^2=0

We add all the numbers together, and all the variables

135x+(-250x)+5*1125x^2=0

Wy multiply elements

5625x^2+135x+(-250x)=0

We get rid of parentheses

5625x^2+135x-250x=0

We add all the numbers together, and all the variables

5625x^2-115x=0

a = 5625; b = -115; c = 0;
Δ = b2-4ac
Δ = -1152-4·5625·0
Δ = 13225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13225}=115$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-115)-115}{2*5625}=\frac{0}{11250}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-115)+115}{2*5625}=\frac{230}{11250}
=23/1125
$