-6r^2-2r+9=0

Solution for -6r^2-2r+9=0 equation:

-6r^2-2r+9=0

a = -6; b = -2; c = +9;
Δ = b2-4ac
Δ = -22-4·(-6)·9
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{55}}{2*-6}=\frac{2-2\sqrt{55}}{-12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{55}}{2*-6}=\frac{2+2\sqrt{55}}{-12}
$