x+1/3x+2/3x-4=30

Solution for x+1/3x+2/3x-4=30 equation:

x+1/3x+2/3x-4=30

We move all terms to the left:

x+1/3x+2/3x-4-(30)=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+2/3x-34=0

We multiply all the terms by the denominator


x*3x-34*3x+1+2=0

We add all the numbers together, and all the variables

x*3x-34*3x+3=0

Wy multiply elements

3x^2-102x+3=0

a = 3; b = -102; c = +3;
Δ = b2-4ac
Δ = -1022-4·3·3
Δ = 10368
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:

$\sqrt{\Delta}=\sqrt{10368}=\sqrt{5184*2}=\sqrt{5184}*\sqrt{2}=72\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-72\sqrt{2}}{2*3}=\frac{102-72\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+72\sqrt{2}}{2*3}=\frac{102+72\sqrt{2}}{6}
$