x+1+x+2+x+3=1/2x+1+33

Solution for x+1+x+2+x+3=1/2x+1+33 equation:

x+1+x+2+x+3=1/2x+1+33

We move all terms to the left:

x+1+x+2+x+3-(1/2x+1+33)=0


Domain of the equation: 2x+1+33)!=0

We move all terms containing x to the left, all other terms to the right

2x+33)!=-1

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

3x-(1/2x+34)+6=0

We get rid of parentheses

3x-1/2x-34+6=0

We multiply all the terms by the denominator


3x*2x-34*2x+6*2x-1=0

Wy multiply elements

6x^2-68x+12x-1=0

We add all the numbers together, and all the variables

6x^2-56x-1=0

a = 6; b = -56; c = -1;
Δ = b2-4ac
Δ = -562-4·6·(-1)
Δ = 3160
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:

$\sqrt{\Delta}=\sqrt{3160}=\sqrt{4*790}=\sqrt{4}*\sqrt{790}=2\sqrt{790}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{790}}{2*6}=\frac{56-2\sqrt{790}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{790}}{2*6}=\frac{56+2\sqrt{790}}{12}
$