2/5x-3=2-4/9x

Solution for 2/5x-3=2-4/9x equation:

2/5x-3=2-4/9x

We move all terms to the left:

2/5x-3-(2-4/9x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(-4/9x+2)-3=0

We get rid of parentheses

2/5x+4/9x-2-3=0

We calculate fractions


18x/45x^2+20x/45x^2-2-3=0

We add all the numbers together, and all the variables

18x/45x^2+20x/45x^2-5=0

We multiply all the terms by the denominator


18x+20x-5*45x^2=0

We add all the numbers together, and all the variables

38x-5*45x^2=0

Wy multiply elements

-225x^2+38x=0

a = -225; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·(-225)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*-225}=\frac{-76}{-450}
=38/225
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*-225}=\frac{0}{-450}
=0
$