8+9(-3+4r)r=9

Solution for 8+9(-3+4r)r=9 equation:

8+9(-3+4r)r=9

We move all terms to the left:

8+9(-3+4r)r-(9)=0

We add all the numbers together, and all the variables

9(4r-3)r+8-9=0

We add all the numbers together, and all the variables

9(4r-3)r-1=0

We multiply parentheses

36r^2-27r-1=0

a = 36; b = -27; c = -1;
Δ = b2-4ac
Δ = -272-4·36·(-1)
Δ = 873
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:

$\sqrt{\Delta}=\sqrt{873}=\sqrt{9*97}=\sqrt{9}*\sqrt{97}=3\sqrt{97}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{97}}{2*36}=\frac{27-3\sqrt{97}}{72}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{97}}{2*36}=\frac{27+3\sqrt{97}}{72}
$