5x/(6x+7)=2x

Solution for 5x/(6x+7)=2x equation:

5x/(6x+7)=2x

We move all terms to the left:

5x/(6x+7)-(2x)=0


Domain of the equation: (6x+7)!=0

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

6x!=-7

x!=-7/6

x!=-1+1/6

x∈R


We add all the numbers together, and all the variables

-2x+5x/(6x+7)=0

We multiply all the terms by the denominator


-2x*(6x+7)+5x=0

We add all the numbers together, and all the variables

5x-2x*(6x+7)=0

We multiply parentheses

-12x^2+5x-14x=0

We add all the numbers together, and all the variables

-12x^2-9x=0

a = -12; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-12)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-12}=\frac{18}{-24}
=-3/4
$