16-1/2x=3/x+1

Solution for 16-1/2x=3/x+1 equation:

16-1/2x=3/x+1

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

-1/2x-3/x-1+16=0

We calculate fractions


(-x)/2x^2+(-6x)/2x^2-1+16=0

We add all the numbers together, and all the variables

(-1x)/2x^2+(-6x)/2x^2-1+16=0

We add all the numbers together, and all the variables

(-1x)/2x^2+(-6x)/2x^2+15=0

We multiply all the terms by the denominator


(-1x)+(-6x)+15*2x^2=0

Wy multiply elements

30x^2+(-1x)+(-6x)=0

We get rid of parentheses

30x^2-1x-6x=0

We add all the numbers together, and all the variables

30x^2-7x=0

a = 30; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·30·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*30}=\frac{14}{60}
=7/30
$