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∈R


We get rid of parentheses

x-3x-1/x+7=0

We multiply all the terms by the denominator


x*x-3x*x+7*x-1=0

We add all the numbers together, and all the variables

7x+x*x-3x*x-1=0

Wy multiply elements

x^2-3x^2+7x-1=0

We add all the numbers together, and all the variables

-2x^2+7x-1=0

a = -2; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·(-2)·(-1)
Δ = 41
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{41}}{2*-2}=\frac{-7-\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{41}}{2*-2}=\frac{-7+\sqrt{41}}{-4}
$