5m(5m+8)=16

Solution for 5m(5m+8)=16 equation:

5m(5m+8)=16

We move all terms to the left:

5m(5m+8)-(16)=0

We multiply parentheses

25m^2+40m-16=0

a = 25; b = 40; c = -16;
Δ = b2-4ac
Δ = 402-4·25·(-16)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40\sqrt{2}}{2*25}=\frac{-40-40\sqrt{2}}{50}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40\sqrt{2}}{2*25}=\frac{-40+40\sqrt{2}}{50}
$