6x+1/3x=171

Solution for 6x+1/3x=171 equation:

6x+1/3x=171

We move all terms to the left:

6x+1/3x-(171)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


6x*3x-171*3x+1=0

Wy multiply elements

18x^2-513x+1=0

a = 18; b = -513; c = +1;
Δ = b2-4ac
Δ = -5132-4·18·1
Δ = 263097
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:

$\sqrt{\Delta}=\sqrt{263097}=\sqrt{9*29233}=\sqrt{9}*\sqrt{29233}=3\sqrt{29233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-513)-3\sqrt{29233}}{2*18}=\frac{513-3\sqrt{29233}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-513)+3\sqrt{29233}}{2*18}=\frac{513+3\sqrt{29233}}{36}
$