9k(10k-1)=0

Solution for 9k(10k-1)=0 equation:

9k(10k-1)=0

We multiply parentheses

90k^2-9k=0

a = 90; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·90·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*90}=\frac{0}{180}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*90}=\frac{18}{180}
=1/10
$