3x+1/3x=70

Solution for 3x+1/3x=70 equation:

3x+1/3x=70

We move all terms to the left:

3x+1/3x-(70)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-70*3x+1=0

Wy multiply elements

9x^2-210x+1=0

a = 9; b = -210; c = +1;
Δ = b2-4ac
Δ = -2102-4·9·1
Δ = 44064
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:

$\sqrt{\Delta}=\sqrt{44064}=\sqrt{1296*34}=\sqrt{1296}*\sqrt{34}=36\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-36\sqrt{34}}{2*9}=\frac{210-36\sqrt{34}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+36\sqrt{34}}{2*9}=\frac{210+36\sqrt{34}}{18}
$