2/r+4=4r

Solution for 2/r+4=4r equation:

2/r+4=4r

We move all terms to the left:

2/r+4-(4r)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

-4r+2/r+4=0

We multiply all the terms by the denominator


-4r*r+4*r+2=0

We add all the numbers together, and all the variables

4r-4r*r+2=0

Wy multiply elements

-4r^2+4r+2=0

a = -4; b = 4; c = +2;
Δ = b2-4ac
Δ = 42-4·(-4)·2
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{3}}{2*-4}=\frac{-4-4\sqrt{3}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{3}}{2*-4}=\frac{-4+4\sqrt{3}}{-8}
$