5m^2+12m+1=0

Solution for 5m^2+12m+1=0 equation:

5m^2+12m+1=0

a = 5; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·5·1
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{31}}{2*5}=\frac{-12-2\sqrt{31}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{31}}{2*5}=\frac{-12+2\sqrt{31}}{10}
$