9r^2-12r=18

Solution for 9r^2-12r=18 equation:

9r^2-12r=18

We move all terms to the left:

9r^2-12r-(18)=0

a = 9; b = -12; c = -18;
Δ = b2-4ac
Δ = -122-4·9·(-18)
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{22}}{2*9}=\frac{12-6\sqrt{22}}{18}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{22}}{2*9}=\frac{12+6\sqrt{22}}{18}
$