X+3+x+3+1/2x+1/2x=23

Solution for X+3+x+3+1/2x+1/2x=23 equation:

X+3+X+3+1/2X+1/2X=23

We move all terms to the left:

X+3+X+3+1/2X+1/2X-(23)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

2X+1/2X+1/2X-17=0

We multiply all the terms by the denominator


2X*2X-17*2X+1+1=0

We add all the numbers together, and all the variables

2X*2X-17*2X+2=0

Wy multiply elements

4X^2-34X+2=0

a = 4; b = -34; c = +2;
Δ = b2-4ac
Δ = -342-4·4·2
Δ = 1124
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:

$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{281}}{2*4}=\frac{34-2\sqrt{281}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{281}}{2*4}=\frac{34+2\sqrt{281}}{8}
$