1/2x+5=-7/3x-1

Solution for 1/2x+5=-7/3x-1 equation:

1/2x+5=-7/3x-1

We move all terms to the left:

1/2x+5-(-7/3x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

1/2x+7/3x+1+5=0

We calculate fractions


3x/6x^2+14x/6x^2+1+5=0

We add all the numbers together, and all the variables

3x/6x^2+14x/6x^2+6=0

We multiply all the terms by the denominator


3x+14x+6*6x^2=0

We add all the numbers together, and all the variables

17x+6*6x^2=0

Wy multiply elements

36x^2+17x=0

a = 36; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·36·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*36}=\frac{-34}{72}
=-17/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*36}=\frac{0}{72}
=0
$