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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 7x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


14x/21x^2+(-15x)/21x^2+3+5=0

We add all the numbers together, and all the variables

14x/21x^2+(-15x)/21x^2+8=0

We multiply all the terms by the denominator


14x+(-15x)+8*21x^2=0

Wy multiply elements

168x^2+14x+(-15x)=0

We get rid of parentheses

168x^2+14x-15x=0

We add all the numbers together, and all the variables

168x^2-1x=0

a = 168; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·168·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*168}=\frac{0}{336}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*168}=\frac{2}{336}
=1/168
$