m^2-25=-12m

Solution for m^2-25=-12m equation:

m^2-25=-12m

We move all terms to the left:

m^2-25-(-12m)=0

We get rid of parentheses

m^2+12m-25=0

a = 1; b = 12; c = -25;
Δ = b2-4ac
Δ = 122-4·1·(-25)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{61}}{2*1}=\frac{-12-2\sqrt{61}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{61}}{2*1}=\frac{-12+2\sqrt{61}}{2}
$