m^2-8m-72=-4

Solution for m^2-8m-72=-4 equation:

m^2-8m-72=-4

We move all terms to the left:

m^2-8m-72-(-4)=0

We add all the numbers together, and all the variables

m^2-8m-68=0

a = 1; b = -8; c = -68;
Δ = b2-4ac
Δ = -82-4·1·(-68)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{21}}{2*1}=\frac{8-4\sqrt{21}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{21}}{2*1}=\frac{8+4\sqrt{21}}{2}
$