-r+3r^2-9=0

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

-r+3r^2-9=0

We add all the numbers together, and all the variables

3r^2-1r-9=0

a = 3; b = -1; c = -9;
Δ = b2-4ac
Δ = -12-4·3·(-9)
Δ = 109
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{-(-1)-\sqrt{109}}{2*3}=\frac{1-\sqrt{109}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{109}}{2*3}=\frac{1+\sqrt{109}}{6}
$