5m^2+16m+5=0

Solution for 5m^2+16m+5=0 equation:

5m^2+16m+5=0

a = 5; b = 16; c = +5;
Δ = b2-4ac
Δ = 162-4·5·5
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{39}}{2*5}=\frac{-16-2\sqrt{39}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{39}}{2*5}=\frac{-16+2\sqrt{39}}{10}
$