x+x-35+x-46=1/2x

Solution for x+x-35+x-46=1/2x equation:

x+x-35+x-46=1/2x

We move all terms to the left:

x+x-35+x-46-(1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+x+x-(+1/2x)-35-46=0

We add all the numbers together, and all the variables

3x-(+1/2x)-81=0

We get rid of parentheses

3x-1/2x-81=0

We multiply all the terms by the denominator


3x*2x-81*2x-1=0

Wy multiply elements

6x^2-162x-1=0

a = 6; b = -162; c = -1;
Δ = b2-4ac
Δ = -1622-4·6·(-1)
Δ = 26268
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:

$\sqrt{\Delta}=\sqrt{26268}=\sqrt{4*6567}=\sqrt{4}*\sqrt{6567}=2\sqrt{6567}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-2\sqrt{6567}}{2*6}=\frac{162-2\sqrt{6567}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+2\sqrt{6567}}{2*6}=\frac{162+2\sqrt{6567}}{12}
$