r(r+6)=(r*r)(12)

Solution for r(r+6)=(r*r)(12) equation:

r(r+6)=(r*r)(12)

We move all terms to the left:

r(r+6)-((r*r)(12))=0

We add all the numbers together, and all the variables

r(r+6)-((+r*r)12)=0

We multiply parentheses

r^2+6r-((+r*r)12)=0


We calculate terms in parentheses: -((+r*r)12), so:

(+r*r)12

We multiply parentheses

12r^2

Back to the equation:

-(12r^2)


determiningTheFunctionDomain
r^2-12r^2+6r=0

We add all the numbers together, and all the variables

-11r^2+6r=0

a = -11; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-11)·0
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{-(6)-6}{2*-11}=\frac{-12}{-22}
=6/11
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-11}=\frac{0}{-22}
=0
$