x+2x+3+(1/2x)=11

Solution for x+2x+3+(1/2x)=11 equation:

x+2x+3+(1/2x)=11

We move all terms to the left:

x+2x+3+(1/2x)-(11)=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+2x+(+1/2x)+3-11=0

We add all the numbers together, and all the variables

3x+(+1/2x)-8=0

We get rid of parentheses

3x+1/2x-8=0

We multiply all the terms by the denominator


3x*2x-8*2x+1=0

Wy multiply elements

6x^2-16x+1=0

a = 6; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·6·1
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{58}}{2*6}=\frac{16-2\sqrt{58}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{58}}{2*6}=\frac{16+2\sqrt{58}}{12}
$