4/r+4+4r=14

Solution for 4/r+4+4r=14 equation:

4/r+4+4r=14

We move all terms to the left:

4/r+4+4r-(14)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

4r+4/r-10=0

We multiply all the terms by the denominator


4r*r-10*r+4=0

We add all the numbers together, and all the variables

-10r+4r*r+4=0

Wy multiply elements

4r^2-10r+4=0

a = 4; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·4·4
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6}{2*4}=\frac{4}{8}
=1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6}{2*4}=\frac{16}{8}
=2
$