m^2=-14m-24

Solution for m^2=-14m-24 equation:

m^2=-14m-24

We move all terms to the left:

m^2-(-14m-24)=0

We get rid of parentheses

m^2+14m+24=0

a = 1; b = 14; c = +24;
Δ = b2-4ac
Δ = 142-4·1·24
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*1}=\frac{-24}{2}
=-12
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*1}=\frac{-4}{2}
=-2
$