-4x(8x+9)=0

Solution for -4x(8x+9)=0 equation:

-4x(8x+9)=0

We multiply parentheses

-32x^2-36x=0

a = -32; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-32)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-32}=\frac{0}{-64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-32}=\frac{72}{-64}
=-1+1/8
$