3x+7+1/x=6x

Solution for 3x+7+1/x=6x equation:

3x+7+1/x=6x

We move all terms to the left:

3x+7+1/x-(6x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-3x+1/x+7=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

7x-3x*x+1=0

Wy multiply elements

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

a = -3; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-3)·1
Δ = 61
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{61}}{2*-3}=\frac{-7-\sqrt{61}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{61}}{2*-3}=\frac{-7+\sqrt{61}}{-6}
$