2/3x+x=-1/3x+14

Solution for 2/3x+x=-1/3x+14 equation:

2/3x+x=-1/3x+14

We move all terms to the left:

2/3x+x-(-1/3x+14)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x+14)!=0

x∈R


We add all the numbers together, and all the variables

x+2/3x-(-1/3x+14)=0

We get rid of parentheses

x+2/3x+1/3x-14=0

We multiply all the terms by the denominator


x*3x-14*3x+2+1=0

We add all the numbers together, and all the variables

x*3x-14*3x+3=0

Wy multiply elements

3x^2-42x+3=0

a = 3; b = -42; c = +3;
Δ = b2-4ac
Δ = -422-4·3·3
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-24\sqrt{3}}{2*3}=\frac{42-24\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+24\sqrt{3}}{2*3}=\frac{42+24\sqrt{3}}{6}
$