3r^2-9=11r

Solution for 3r^2-9=11r equation:

3r^2-9=11r

We move all terms to the left:

3r^2-9-(11r)=0

a = 3; b = -11; c = -9;
Δ = b2-4ac
Δ = -112-4·3·(-9)
Δ = 229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{229}}{2*3}=\frac{11-\sqrt{229}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{229}}{2*3}=\frac{11+\sqrt{229}}{6}
$