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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/15x^2+5x/15x^2+5+3=0

We add all the numbers together, and all the variables

6x/15x^2+5x/15x^2+8=0

We multiply all the terms by the denominator


6x+5x+8*15x^2=0

We add all the numbers together, and all the variables

11x+8*15x^2=0

Wy multiply elements

120x^2+11x=0

a = 120; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·120·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*120}=\frac{-22}{240}
=-11/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*120}=\frac{0}{240}
=0
$