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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-10x)/54x^2+27x/54x^2+10x/54x^2+7=0

We multiply all the terms by the denominator


(-10x)+27x+10x+7*54x^2=0

We add all the numbers together, and all the variables

37x+(-10x)+7*54x^2=0

Wy multiply elements

378x^2+37x+(-10x)=0

We get rid of parentheses

378x^2+37x-10x=0

We add all the numbers together, and all the variables

378x^2+27x=0

a = 378; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·378·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*378}=\frac{-54}{756}
=-1/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*378}=\frac{0}{756}
=0
$