X+3=1/2y

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

X+3=1/2X

We move all terms to the left:

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

We get rid of parentheses

X-1/2X+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

2X^2+6X-1=0

a = 2; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·2·(-1)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{11}}{2*2}=\frac{-6-2\sqrt{11}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{11}}{2*2}=\frac{-6+2\sqrt{11}}{4}
$