3x+2/3x=98

Solution for 3x+2/3x=98 equation:

3x+2/3x=98

We move all terms to the left:

3x+2/3x-(98)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-98*3x+2=0

Wy multiply elements

9x^2-294x+2=0

a = 9; b = -294; c = +2;
Δ = b2-4ac
Δ = -2942-4·9·2
Δ = 86364
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:

$\sqrt{\Delta}=\sqrt{86364}=\sqrt{36*2399}=\sqrt{36}*\sqrt{2399}=6\sqrt{2399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-294)-6\sqrt{2399}}{2*9}=\frac{294-6\sqrt{2399}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-294)+6\sqrt{2399}}{2*9}=\frac{294+6\sqrt{2399}}{18}
$