r=6/6r-6

Solution for r=6/6r-6 equation:

r=6/6r-6

We move all terms to the left:

r-(6/6r-6)=0


Domain of the equation: 6r-6)!=0

r∈R


We get rid of parentheses

r-6/6r+6=0

We multiply all the terms by the denominator


r*6r+6*6r-6=0

Wy multiply elements

6r^2+36r-6=0

a = 6; b = 36; c = -6;
Δ = b2-4ac
Δ = 362-4·6·(-6)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{10}}{2*6}=\frac{-36-12\sqrt{10}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{10}}{2*6}=\frac{-36+12\sqrt{10}}{12}
$