3x+2/3x=49

Solution for 3x+2/3x=49 equation:

3x+2/3x=49

We move all terms to the left:

3x+2/3x-(49)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-49*3x+2=0

Wy multiply elements

9x^2-147x+2=0

a = 9; b = -147; c = +2;
Δ = b2-4ac
Δ = -1472-4·9·2
Δ = 21537
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:

$\sqrt{\Delta}=\sqrt{21537}=\sqrt{9*2393}=\sqrt{9}*\sqrt{2393}=3\sqrt{2393}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-147)-3\sqrt{2393}}{2*9}=\frac{147-3\sqrt{2393}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-147)+3\sqrt{2393}}{2*9}=\frac{147+3\sqrt{2393}}{18}
$