1/9x+2=1/5x-2

Solution for 1/9x+2=1/5x-2 equation:

1/9x+2=1/5x-2

We move all terms to the left:

1/9x+2-(1/5x-2)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 5x-2)!=0

x∈R


We get rid of parentheses

1/9x-1/5x+2+2=0

We calculate fractions


5x/45x^2+(-9x)/45x^2+2+2=0

We add all the numbers together, and all the variables

5x/45x^2+(-9x)/45x^2+4=0

We multiply all the terms by the denominator


5x+(-9x)+4*45x^2=0

Wy multiply elements

180x^2+5x+(-9x)=0

We get rid of parentheses

180x^2+5x-9x=0

We add all the numbers together, and all the variables

180x^2-4x=0

a = 180; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·180·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*180}=\frac{0}{360}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*180}=\frac{8}{360}
=1/45
$