3/x=3/(4x)+3

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

3/x=3/(4x)+3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

3/x-3/4x-3=0

We calculate fractions


12x/4x^2+(-3x)/4x^2-3=0

We multiply all the terms by the denominator


12x+(-3x)-3*4x^2=0

Wy multiply elements

-12x^2+12x+(-3x)=0

We get rid of parentheses

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