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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


10x/15x^2+3x/15x^2+1+5=0

We add all the numbers together, and all the variables

10x/15x^2+3x/15x^2+6=0

We multiply all the terms by the denominator


10x+3x+6*15x^2=0

We add all the numbers together, and all the variables

13x+6*15x^2=0

Wy multiply elements

90x^2+13x=0

a = 90; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·90·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*90}=\frac{-26}{180}
=-13/90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*90}=\frac{0}{180}
=0
$