x+1/6x=90

Solution for x+1/6x=90 equation:

x+1/6x=90

We move all terms to the left:

x+1/6x-(90)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-90*6x+1=0

Wy multiply elements

6x^2-540x+1=0

a = 6; b = -540; c = +1;
Δ = b2-4ac
Δ = -5402-4·6·1
Δ = 291576
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:

$\sqrt{\Delta}=\sqrt{291576}=\sqrt{4*72894}=\sqrt{4}*\sqrt{72894}=2\sqrt{72894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72894}}{2*6}=\frac{540-2\sqrt{72894}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72894}}{2*6}=\frac{540+2\sqrt{72894}}{12}
$