5/x+1/3x-4=12

Solution for 5/x+1/3x-4=12 equation:

5/x+1/3x-4=12

We move all terms to the left:

5/x+1/3x-4-(12)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/x+1/3x-16=0

We calculate fractions


15x/3x^2+x/3x^2-16=0

We multiply all the terms by the denominator


15x+x-16*3x^2=0

We add all the numbers together, and all the variables

16x-16*3x^2=0

Wy multiply elements

-48x^2+16x=0

a = -48; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-48)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-48}=\frac{-32}{-96}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-48}=\frac{0}{-96}
=0
$