6r(9r-4)=0

Solution for 6r(9r-4)=0 equation:

6r(9r-4)=0

We multiply parentheses

54r^2-24r=0

a = 54; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·54·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*54}=\frac{0}{108}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*54}=\frac{48}{108}
=4/9
$