r=5/3r+23

Solution for r=5/3r+23 equation:

r=5/3r+23

We move all terms to the left:

r-(5/3r+23)=0


Domain of the equation: 3r+23)!=0

r∈R


We get rid of parentheses

r-5/3r-23=0

We multiply all the terms by the denominator


r*3r-23*3r-5=0

Wy multiply elements

3r^2-69r-5=0

a = 3; b = -69; c = -5;
Δ = b2-4ac
Δ = -692-4·3·(-5)
Δ = 4821
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-\sqrt{4821}}{2*3}=\frac{69-\sqrt{4821}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+\sqrt{4821}}{2*3}=\frac{69+\sqrt{4821}}{6}
$