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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

14x/21x^2+(-15x)/21x^2+7=0

We multiply all the terms by the denominator


14x+(-15x)+7*21x^2=0

Wy multiply elements

147x^2+14x+(-15x)=0

We get rid of parentheses

147x^2+14x-15x=0

We add all the numbers together, and all the variables

147x^2-1x=0

a = 147; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·147·0
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*147}=\frac{0}{294}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*147}=\frac{2}{294}
=1/147
$