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

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

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

We move all terms to the left:

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


Domain of the equation: (3x+2)!=0

We move all terms containing x to the left, all other terms to the right

3x!=-2

x!=-2/3

x!=-2/3

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We multiply parentheses

-6x^2-4x+(7x+5)=0

We get rid of parentheses

-6x^2-4x+7x+5=0

We add all the numbers together, and all the variables

-6x^2+3x+5=0

a = -6; b = 3; c = +5;
Δ = b2-4ac
Δ = 32-4·(-6)·5
Δ = 129
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{-(3)-\sqrt{129}}{2*-6}=\frac{-3-\sqrt{129}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{129}}{2*-6}=\frac{-3+\sqrt{129}}{-12}
$