8m^2+16m+32=40

Solution for 8m^2+16m+32=40 equation:

8m^2+16m+32=40

We move all terms to the left:

8m^2+16m+32-(40)=0

We add all the numbers together, and all the variables

8m^2+16m-8=0

a = 8; b = 16; c = -8;
Δ = b2-4ac
Δ = 162-4·8·(-8)
Δ = 512
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{2}}{2*8}=\frac{-16-16\sqrt{2}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{2}}{2*8}=\frac{-16+16\sqrt{2}}{16}
$