9r^2-12r-45=0

Solution for 9r^2-12r-45=0 equation:

9r^2-12r-45=0

a = 9; b = -12; c = -45;
Δ = b2-4ac
Δ = -122-4·9·(-45)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-42}{2*9}=\frac{-30}{18}
=-1+2/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+42}{2*9}=\frac{54}{18}
=3
$