x+1/6x=49

Solution for x+1/6x=49 equation:

x+1/6x=49

We move all terms to the left:

x+1/6x-(49)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-49*6x+1=0

Wy multiply elements

6x^2-294x+1=0

a = 6; b = -294; c = +1;
Δ = b2-4ac
Δ = -2942-4·6·1
Δ = 86412
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:

$\sqrt{\Delta}=\sqrt{86412}=\sqrt{4*21603}=\sqrt{4}*\sqrt{21603}=2\sqrt{21603}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-294)-2\sqrt{21603}}{2*6}=\frac{294-2\sqrt{21603}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-294)+2\sqrt{21603}}{2*6}=\frac{294+2\sqrt{21603}}{12}
$