3/5x-2/9x=34

Solution for 3/5x-2/9x=34 equation:

3/5x-2/9x=34

We move all terms to the left:

3/5x-2/9x-(34)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We calculate fractions


27x/45x^2+(-10x)/45x^2-34=0

We multiply all the terms by the denominator


27x+(-10x)-34*45x^2=0

Wy multiply elements

-1530x^2+27x+(-10x)=0

We get rid of parentheses

-1530x^2+27x-10x=0

We add all the numbers together, and all the variables

-1530x^2+17x=0

a = -1530; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-1530)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-1530}=\frac{-34}{-3060}
=1/90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-1530}=\frac{0}{-3060}
=0
$