x+1/3x=184

Solution for x+1/3x=184 equation:

x+1/3x=184

We move all terms to the left:

x+1/3x-(184)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-184*3x+1=0

Wy multiply elements

3x^2-552x+1=0

a = 3; b = -552; c = +1;
Δ = b2-4ac
Δ = -5522-4·3·1
Δ = 304692
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:

$\sqrt{\Delta}=\sqrt{304692}=\sqrt{4*76173}=\sqrt{4}*\sqrt{76173}=2\sqrt{76173}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-552)-2\sqrt{76173}}{2*3}=\frac{552-2\sqrt{76173}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-552)+2\sqrt{76173}}{2*3}=\frac{552+2\sqrt{76173}}{6}
$