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

Solution for 5/x+(x-4)/3x=4 equation:

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


15x/3x^2+(x^2-4x)/3x^2-4=0

We multiply all the terms by the denominator


15x+(x^2-4x)-4*3x^2=0

Wy multiply elements

-12x^2+15x+(x^2-4x)=0

We get rid of parentheses

-12x^2+x^2+15x-4x=0

We add all the numbers together, and all the variables

-11x^2+11x=0

a = -11; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-11)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-11}=\frac{-22}{-22}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-11}=\frac{0}{-22}
=0
$