16-1/x=3/4x+1

Solution for 16-1/x=3/4x+1 equation:

16-1/x=3/4x+1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

-1/x-3/4x-1+16=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

60x^2+(-4x)+(-3x)=0

We get rid of parentheses

60x^2-4x-3x=0

We add all the numbers together, and all the variables

60x^2-7x=0

a = 60; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·60·0
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*60}=\frac{0}{120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*60}=\frac{14}{120}
=7/60
$