m2=125

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Solution for m2=125 equation:



m2=125
We move all terms to the left:
m2-(125)=0
We add all the numbers together, and all the variables
m^2-125=0
a = 1; b = 0; c = -125;
Δ = b2-4ac
Δ = 02-4·1·(-125)
Δ = 500
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:
$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{5}}{2*1}=\frac{0-10\sqrt{5}}{2} =-\frac{10\sqrt{5}}{2} =-5\sqrt{5} $
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{5}}{2*1}=\frac{0+10\sqrt{5}}{2} =\frac{10\sqrt{5}}{2} =5\sqrt{5} $

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