3/16x=1/x+13

Solution for 3/16x=1/x+13 equation:

3/16x=1/x+13

We move all terms to the left:

3/16x-(1/x+13)=0


Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R



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

x∈R


We get rid of parentheses

3/16x-1/x-13=0

We calculate fractions


3x/16x^2+(-16x)/16x^2-13=0

We multiply all the terms by the denominator


3x+(-16x)-13*16x^2=0

Wy multiply elements

-208x^2+3x+(-16x)=0

We get rid of parentheses

-208x^2+3x-16x=0

We add all the numbers together, and all the variables

-208x^2-13x=0

a = -208; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-208)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*-208}=\frac{0}{-416}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-208}=\frac{26}{-416}
=-1/16
$