33=12r(9-r)

Solution for 33=12r(9-r) equation:

33=12r(9-r)

We move all terms to the left:

33-(12r(9-r))=0

We add all the numbers together, and all the variables

-(12r(-1r+9))+33=0


We calculate terms in parentheses: -(12r(-1r+9)), so:

12r(-1r+9)

We multiply parentheses

-12r^2+108r

Back to the equation:

-(-12r^2+108r)


We get rid of parentheses

12r^2-108r+33=0

a = 12; b = -108; c = +33;
Δ = b2-4ac
Δ = -1082-4·12·33
Δ = 10080
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:

$\sqrt{\Delta}=\sqrt{10080}=\sqrt{144*70}=\sqrt{144}*\sqrt{70}=12\sqrt{70}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-12\sqrt{70}}{2*12}=\frac{108-12\sqrt{70}}{24}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+12\sqrt{70}}{2*12}=\frac{108+12\sqrt{70}}{24}
$