X+4=1/3y

Solution for X+4=1/3y equation:

X+4=1/3X

We move all terms to the left:

X+4-(1/3X)=0


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+1/3X)+4=0

We get rid of parentheses

X-1/3X+4=0

We multiply all the terms by the denominator


X*3X+4*3X-1=0

Wy multiply elements

3X^2+12X-1=0

a = 3; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·3·(-1)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{39}}{2*3}=\frac{-12-2\sqrt{39}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{39}}{2*3}=\frac{-12+2\sqrt{39}}{6}
$