(9k-1)(-2k+3)=0

Solution for (9k-1)(-2k+3)=0 equation:

(9k-1)(-2k+3)=0

We multiply parentheses ..

(-18k^2+27k+2k-3)=0

We get rid of parentheses

-18k^2+27k+2k-3=0

We add all the numbers together, and all the variables

-18k^2+29k-3=0

a = -18; b = 29; c = -3;
Δ = b2-4ac
Δ = 292-4·(-18)·(-3)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-25}{2*-18}=\frac{-54}{-36}
=1+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+25}{2*-18}=\frac{-4}{-36}
=1/9
$