3r+4=30/r

Solution for 3r+4=30/r equation:

3r+4=30/r

We move all terms to the left:

3r+4-(30/r)=0


Domain of the equation: r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

3r-(+30/r)+4=0

We get rid of parentheses

3r-30/r+4=0

We multiply all the terms by the denominator


3r*r+4*r-30=0

We add all the numbers together, and all the variables

4r+3r*r-30=0

Wy multiply elements

3r^2+4r-30=0

a = 3; b = 4; c = -30;
Δ = b2-4ac
Δ = 42-4·3·(-30)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{94}}{2*3}=\frac{-4-2\sqrt{94}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{94}}{2*3}=\frac{-4+2\sqrt{94}}{6}
$