m2+24m+29=0

Solution for m2+24m+29=0 equation:

m2+24m+29=0

We add all the numbers together, and all the variables

m^2+24m+29=0

a = 1; b = 24; c = +29;
Δ = b2-4ac
Δ = 242-4·1·29
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{115}}{2*1}=\frac{-24-2\sqrt{115}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{115}}{2*1}=\frac{-24+2\sqrt{115}}{2}
$