6=r(15-6r)

Solution for 6=r(15-6r) equation:

6=r(15-6r)

We move all terms to the left:

6-(r(15-6r))=0

We add all the numbers together, and all the variables

-(r(-6r+15))+6=0


We calculate terms in parentheses: -(r(-6r+15)), so:

r(-6r+15)

We multiply parentheses

-6r^2+15r

Back to the equation:

-(-6r^2+15r)


We get rid of parentheses

6r^2-15r+6=0

a = 6; b = -15; c = +6;
Δ = b2-4ac
Δ = -152-4·6·6
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*6}=\frac{6}{12}
=1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*6}=\frac{24}{12}
=2
$