m2=127

Solution for m2=127 equation:

m2=127

We move all terms to the left:

m2-(127)=0

We add all the numbers together, and all the variables

m^2-127=0

a = 1; b = 0; c = -127;
Δ = b2-4ac
Δ = 02-4·1·(-127)
Δ = 508
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:

$\sqrt{\Delta}=\sqrt{508}=\sqrt{4*127}=\sqrt{4}*\sqrt{127}=2\sqrt{127}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{127}}{2*1}=\frac{0-2\sqrt{127}}{2}
=-\frac{2\sqrt{127}}{2}
=-\sqrt{127}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{127}}{2*1}=\frac{0+2\sqrt{127}}{2}
=\frac{2\sqrt{127}}{2}
=\sqrt{127}
$