3r^2-2r-9=0

Solution for 3r^2-2r-9=0 equation:

3r^2-2r-9=0

a = 3; b = -2; c = -9;
Δ = b2-4ac
Δ = -22-4·3·(-9)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{7}}{2*3}=\frac{2-4\sqrt{7}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{7}}{2*3}=\frac{2+4\sqrt{7}}{6}
$