-9x(4x-1)=0

Solution for -9x(4x-1)=0 equation:

-9x(4x-1)=0

We multiply parentheses

-36x^2+9x=0

a = -36; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-36)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-36}=\frac{-18}{-72}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-36}=\frac{0}{-72}
=0
$