m^2-6m-78=-4

Solution for m^2-6m-78=-4 equation:

m^2-6m-78=-4

We move all terms to the left:

m^2-6m-78-(-4)=0

We add all the numbers together, and all the variables

m^2-6m-74=0

a = 1; b = -6; c = -74;
Δ = b2-4ac
Δ = -62-4·1·(-74)
Δ = 332
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:

$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{83}}{2*1}=\frac{6-2\sqrt{83}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{83}}{2*1}=\frac{6+2\sqrt{83}}{2}
$