3x+1/3x=60

Solution for 3x+1/3x=60 equation:

3x+1/3x=60

We move all terms to the left:

3x+1/3x-(60)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-60*3x+1=0

Wy multiply elements

9x^2-180x+1=0

a = 9; b = -180; c = +1;
Δ = b2-4ac
Δ = -1802-4·9·1
Δ = 32364
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:

$\sqrt{\Delta}=\sqrt{32364}=\sqrt{36*899}=\sqrt{36}*\sqrt{899}=6\sqrt{899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-6\sqrt{899}}{2*9}=\frac{180-6\sqrt{899}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+6\sqrt{899}}{2*9}=\frac{180+6\sqrt{899}}{18}
$