3x/(4x+13)=x

Solution for 3x/(4x+13)=x equation:

3x/(4x+13)=x

We move all terms to the left:

3x/(4x+13)-(x)=0


Domain of the equation: (4x+13)!=0

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

4x!=-13

x!=-13/4

x!=-3+1/4

x∈R


We add all the numbers together, and all the variables

-1x+3x/(4x+13)=0

We multiply all the terms by the denominator


-1x*(4x+13)+3x=0

We add all the numbers together, and all the variables

3x-1x*(4x+13)=0

We multiply parentheses

-4x^2+3x-13x=0

We add all the numbers together, and all the variables

-4x^2-10x=0

a = -4; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-4)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-4}=\frac{20}{-8}
=-2+1/2
$