X=4/y+2

Solution for X=4/y+2 equation:

X=4/X+2

We move all terms to the left:

X-(4/X+2)=0


Domain of the equation: X+2)!=0

X∈R


We get rid of parentheses

X-4/X-2=0

We multiply all the terms by the denominator


X*X-2*X-4=0

We add all the numbers together, and all the variables

-2X+X*X-4=0

Wy multiply elements

X^2-2X-4=0

a = 1; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·1·(-4)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{5}}{2*1}=\frac{2-2\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{5}}{2*1}=\frac{2+2\sqrt{5}}{2}
$