2m(4m+3)=0

Solution for 2m(4m+3)=0 equation:

2m(4m+3)=0

We multiply parentheses

8m^2+6m=0

a = 8; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·8·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*8}=\frac{-12}{16}
=-3/4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*8}=\frac{0}{16}
=0
$