3/5x-17/45=2/9x

Solution for 3/5x-17/45=2/9x equation:

3/5x-17/45=2/9x

We move all terms to the left:

3/5x-17/45-(2/9x)=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

3/5x-(+2/9x)-17/45=0

We get rid of parentheses

3/5x-2/9x-17/45=0

We calculate fractions


(-6885x^2)/8100x^2+4860x/8100x^2+(-1800x)/8100x^2=0

We multiply all the terms by the denominator


(-6885x^2)+4860x+(-1800x)=0

We get rid of parentheses

-6885x^2+4860x-1800x=0

We add all the numbers together, and all the variables

-6885x^2+3060x=0

a = -6885; b = 3060; c = 0;
Δ = b2-4ac
Δ = 30602-4·(-6885)·0
Δ = 9363600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9363600}=3060$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3060)-3060}{2*-6885}=\frac{-6120}{-13770}
=4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3060)+3060}{2*-6885}=\frac{0}{-13770}
=0
$