x+1/3x-2=50

Solution for x+1/3x-2=50 equation:

x+1/3x-2=50

We move all terms to the left:

x+1/3x-2-(50)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/3x-52=0

We multiply all the terms by the denominator


x*3x-52*3x+1=0

Wy multiply elements

3x^2-156x+1=0

a = 3; b = -156; c = +1;
Δ = b2-4ac
Δ = -1562-4·3·1
Δ = 24324
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:

$\sqrt{\Delta}=\sqrt{24324}=\sqrt{4*6081}=\sqrt{4}*\sqrt{6081}=2\sqrt{6081}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-2\sqrt{6081}}{2*3}=\frac{156-2\sqrt{6081}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+2\sqrt{6081}}{2*3}=\frac{156+2\sqrt{6081}}{6}
$