9r^2+3r-6=0

Solution for 9r^2+3r-6=0 equation:

9r^2+3r-6=0

a = 9; b = 3; c = -6;
Δ = b2-4ac
Δ = 32-4·9·(-6)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*9}=\frac{-18}{18}
=-1
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*9}=\frac{12}{18}
=2/3
$