3x+(3/x)=7

Solution for 3x+(3/x)=7 equation:

3x+(3/x)=7

We move all terms to the left:

3x+(3/x)-(7)=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+(+3/x)-7=0

We get rid of parentheses

3x+3/x-7=0

We multiply all the terms by the denominator


3x*x-7*x+3=0

We add all the numbers together, and all the variables

-7x+3x*x+3=0

Wy multiply elements

3x^2-7x+3=0

a = 3; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·3·3
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{13}}{2*3}=\frac{7-\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{13}}{2*3}=\frac{7+\sqrt{13}}{6}
$