3x+1/3x=84

Solution for 3x+1/3x=84 equation:

3x+1/3x=84

We move all terms to the left:

3x+1/3x-(84)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-84*3x+1=0

Wy multiply elements

9x^2-252x+1=0

a = 9; b = -252; c = +1;
Δ = b2-4ac
Δ = -2522-4·9·1
Δ = 63468
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:

$\sqrt{\Delta}=\sqrt{63468}=\sqrt{36*1763}=\sqrt{36}*\sqrt{1763}=6\sqrt{1763}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-6\sqrt{1763}}{2*9}=\frac{252-6\sqrt{1763}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+6\sqrt{1763}}{2*9}=\frac{252+6\sqrt{1763}}{18}
$