r=4/r-2

Solution for r=4/r-2 equation:

r=4/r-2

We move all terms to the left:

r-(4/r-2)=0


Domain of the equation: r-2)!=0

r∈R


We get rid of parentheses

r-4/r+2=0

We multiply all the terms by the denominator


r*r+2*r-4=0

We add all the numbers together, and all the variables

2r+r*r-4=0

Wy multiply elements

r^2+2r-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:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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