2m2+12m+5=0

Solution for 2m2+12m+5=0 equation:

2m^2+12m+5=0

a = 2; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·2·5
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{26}}{2*2}=\frac{-12-2\sqrt{26}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{26}}{2*2}=\frac{-12+2\sqrt{26}}{4}
$