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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


10x/6x^2+15x/6x^2+1=0

We multiply all the terms by the denominator


10x+15x+1*6x^2=0

We add all the numbers together, and all the variables

25x+1*6x^2=0

Wy multiply elements

6x^2+25x=0

a = 6; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·6·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*6}=\frac{-50}{12}
=-4+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*6}=\frac{0}{12}
=0
$