2r(9-9r)=3

Solution for 2r(9-9r)=3 equation:

2r(9-9r)=3

We move all terms to the left:

2r(9-9r)-(3)=0

We add all the numbers together, and all the variables

2r(-9r+9)-3=0

We multiply parentheses

-18r^2+18r-3=0

a = -18; b = 18; c = -3;
Δ = b2-4ac
Δ = 182-4·(-18)·(-3)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{3}}{2*-18}=\frac{-18-6\sqrt{3}}{-36}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{3}}{2*-18}=\frac{-18+6\sqrt{3}}{-36}
$