18r^2-21r+6=0

Solution for 18r^2-21r+6=0 equation:

18r^2-21r+6=0

a = 18; b = -21; c = +6;
Δ = b2-4ac
Δ = -212-4·18·6
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3}{2*18}=\frac{18}{36}
=1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3}{2*18}=\frac{24}{36}
=2/3
$