3x+2/3x=27

Solution for 3x+2/3x=27 equation:

3x+2/3x=27

We move all terms to the left:

3x+2/3x-(27)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-27*3x+2=0

Wy multiply elements

9x^2-81x+2=0

a = 9; b = -81; c = +2;
Δ = b2-4ac
Δ = -812-4·9·2
Δ = 6489
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:

$\sqrt{\Delta}=\sqrt{6489}=\sqrt{9*721}=\sqrt{9}*\sqrt{721}=3\sqrt{721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-3\sqrt{721}}{2*9}=\frac{81-3\sqrt{721}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+3\sqrt{721}}{2*9}=\frac{81+3\sqrt{721}}{18}
$