5/3x+6=2/5x-9

Solution for 5/3x+6=2/5x-9 equation:

5/3x+6=2/5x-9

We move all terms to the left:

5/3x+6-(2/5x-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

5/3x-2/5x+9+6=0

We calculate fractions


25x/15x^2+(-6x)/15x^2+9+6=0

We add all the numbers together, and all the variables

25x/15x^2+(-6x)/15x^2+15=0

We multiply all the terms by the denominator


25x+(-6x)+15*15x^2=0

Wy multiply elements

225x^2+25x+(-6x)=0

We get rid of parentheses

225x^2+25x-6x=0

We add all the numbers together, and all the variables

225x^2+19x=0

a = 225; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·225·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*225}=\frac{-38}{450}
=-19/225
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*225}=\frac{0}{450}
=0
$