5m+24=m^2

Solution for 5m+24=m^2 equation:

5m+24=m^2

We move all terms to the left:

5m+24-(m^2)=0

determiningTheFunctionDomain
-m^2+5m+24=0

We add all the numbers together, and all the variables

-1m^2+5m+24=0

a = -1; b = 5; c = +24;
Δ = b2-4ac
Δ = 52-4·(-1)·24
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*-1}=\frac{-16}{-2}
=+8
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*-1}=\frac{6}{-2}
=-3
$