1/3x-2=-3/5x-9

Solution for 1/3x-2=-3/5x-9 equation:

1/3x-2=-3/5x-9

We move all terms to the left:

1/3x-2-(-3/5x-9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x-9)!=0

x∈R


We get rid of parentheses

1/3x+3/5x+9-2=0

We calculate fractions


5x/15x^2+9x/15x^2+9-2=0

We add all the numbers together, and all the variables

5x/15x^2+9x/15x^2+7=0

We multiply all the terms by the denominator


5x+9x+7*15x^2=0

We add all the numbers together, and all the variables

14x+7*15x^2=0

Wy multiply elements

105x^2+14x=0

a = 105; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·105·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*105}=\frac{-28}{210}
=-2/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*105}=\frac{0}{210}
=0
$