X+1/7x=16

Solution for X+1/7x=16 equation:

X+1/7X=16

We move all terms to the left:

X+1/7X-(16)=0


Domain of the equation: 7X!=0

X!=0/7

X!=0

X∈R


We multiply all the terms by the denominator


X*7X-16*7X+1=0

Wy multiply elements

7X^2-112X+1=0

a = 7; b = -112; c = +1;
Δ = b2-4ac
Δ = -1122-4·7·1
Δ = 12516
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12516}=\sqrt{4*3129}=\sqrt{4}*\sqrt{3129}=2\sqrt{3129}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-2\sqrt{3129}}{2*7}=\frac{112-2\sqrt{3129}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+2\sqrt{3129}}{2*7}=\frac{112+2\sqrt{3129}}{14}
$