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

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

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

We move all terms to the left:

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


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X+1/2X+3-1=0

We add all the numbers together, and all the variables

X+1/2X+2=0

We multiply all the terms by the denominator


X*2X+2*2X+1=0

Wy multiply elements

2X^2+4X+1=0

a = 2; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·2·1
Δ = 8
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:

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