(3x+1)=5/7x

Solution for (3x+1)=5/7x equation:

(3x+1)=5/7x

We move all terms to the left:

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


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3x-5/7x+1=0

We multiply all the terms by the denominator


3x*7x+1*7x-5=0

Wy multiply elements

21x^2+7x-5=0

a = 21; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·21·(-5)
Δ = 469
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{469}}{2*21}=\frac{-7-\sqrt{469}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{469}}{2*21}=\frac{-7+\sqrt{469}}{42}
$