4q(8q+3)=0

Solution for 4q(8q+3)=0 equation:

4q(8q+3)=0

We multiply parentheses

32q^2+12q=0

a = 32; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·32·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*32}=\frac{-24}{64}
=-3/8
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*32}=\frac{0}{64}
=0
$