3x+4=1/x

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

3x+4=1/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3x-1/x+4=0

We multiply all the terms by the denominator


3x*x+4*x-1=0

We add all the numbers together, and all the variables

4x+3x*x-1=0

Wy multiply elements

3x^2+4x-1=0

a = 3; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·3·(-1)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{7}}{2*3}=\frac{-4-2\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{7}}{2*3}=\frac{-4+2\sqrt{7}}{6}
$