x+1/7x=9

Solution for x+1/7x=9 equation:

x+1/7x=9

We move all terms to the left:

x+1/7x-(9)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


x*7x-9*7x+1=0

Wy multiply elements

7x^2-63x+1=0

a = 7; b = -63; c = +1;
Δ = b2-4ac
Δ = -632-4·7·1
Δ = 3941
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{-(-63)-\sqrt{3941}}{2*7}=\frac{63-\sqrt{3941}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{3941}}{2*7}=\frac{63+\sqrt{3941}}{14}
$