3x+2/3x=33

Solution for 3x+2/3x=33 equation:

3x+2/3x=33

We move all terms to the left:

3x+2/3x-(33)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-33*3x+2=0

Wy multiply elements

9x^2-99x+2=0

a = 9; b = -99; c = +2;
Δ = b2-4ac
Δ = -992-4·9·2
Δ = 9729
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:

$\sqrt{\Delta}=\sqrt{9729}=\sqrt{9*1081}=\sqrt{9}*\sqrt{1081}=3\sqrt{1081}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-3\sqrt{1081}}{2*9}=\frac{99-3\sqrt{1081}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+3\sqrt{1081}}{2*9}=\frac{99+3\sqrt{1081}}{18}
$