x+1/3x+2/3x=17

Solution for x+1/3x+2/3x=17 equation:

x+1/3x+2/3x=17

We move all terms to the left:

x+1/3x+2/3x-(17)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-17*3x+1+2=0

We add all the numbers together, and all the variables

x*3x-17*3x+3=0

Wy multiply elements

3x^2-51x+3=0

a = 3; b = -51; c = +3;
Δ = b2-4ac
Δ = -512-4·3·3
Δ = 2565
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:

$\sqrt{\Delta}=\sqrt{2565}=\sqrt{9*285}=\sqrt{9}*\sqrt{285}=3\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{285}}{2*3}=\frac{51-3\sqrt{285}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{285}}{2*3}=\frac{51+3\sqrt{285}}{6}
$