16+4m(2m+6)+3m=4

Solution for 16+4m(2m+6)+3m=4 equation:

16+4m(2m+6)+3m=4

We move all terms to the left:

16+4m(2m+6)+3m-(4)=0

We add all the numbers together, and all the variables

3m+4m(2m+6)+12=0

We multiply parentheses

8m^2+3m+24m+12=0

We add all the numbers together, and all the variables

8m^2+27m+12=0

a = 8; b = 27; c = +12;
Δ = b2-4ac
Δ = 272-4·8·12
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{345}}{2*8}=\frac{-27-\sqrt{345}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{345}}{2*8}=\frac{-27+\sqrt{345}}{16}
$