(m-24)(m+24)=100

Solution for (m-24)(m+24)=100 equation:

(m-24)(m+24)=100

We move all terms to the left:

(m-24)(m+24)-(100)=0

We use the square of the difference formula

m^2-576-100=0

We add all the numbers together, and all the variables

m^2-676=0

a = 1; b = 0; c = -676;
Δ = b2-4ac
Δ = 02-4·1·(-676)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-52}{2*1}=\frac{-52}{2}
=-26
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+52}{2*1}=\frac{52}{2}
=26
$