4/x=1/4x+3

Solution for 4/x=1/4x+3 equation:

4/x=1/4x+3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

4/x-1/4x-3=0

We calculate fractions


16x/4x^2+(-x)/4x^2-3=0

We add all the numbers together, and all the variables

16x/4x^2+(-1x)/4x^2-3=0

We multiply all the terms by the denominator


16x+(-1x)-3*4x^2=0

Wy multiply elements

-12x^2+16x+(-1x)=0

We get rid of parentheses

-12x^2+16x-1x=0

We add all the numbers together, and all the variables

-12x^2+15x=0

a = -12; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-12)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-12}=\frac{-30}{-24}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-12}=\frac{0}{-24}
=0
$