m^2-6m-54=0

Solution for m^2-6m-54=0 equation:

m^2-6m-54=0

a = 1; b = -6; c = -54;
Δ = b2-4ac
Δ = -62-4·1·(-54)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{7}}{2*1}=\frac{6-6\sqrt{7}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{7}}{2*1}=\frac{6+6\sqrt{7}}{2}
$