x=(3x-1/x)^7

Solution for x=(3x-1/x)^7 equation:

x=(3x-1/x)^7

We move all terms to the left:

x-((3x-1/x)^7)=0


Domain of the equation: x)^7)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-((+3x-1/x)^7)=0

We multiply all the terms by the denominator


x*x)^7)-((+3x-1=0

We add all the numbers together, and all the variables

3x+x*x)^7)-((-1=0

Wy multiply elements

x^2+3x-1=0

a = 1; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·1·(-1)
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{-(3)-\sqrt{13}}{2*1}=\frac{-3-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{13}}{2*1}=\frac{-3+\sqrt{13}}{2}
$