m^2-16m-27=-7

Solution for m^2-16m-27=-7 equation:

m^2-16m-27=-7

We move all terms to the left:

m^2-16m-27-(-7)=0

We add all the numbers together, and all the variables

m^2-16m-20=0

a = 1; b = -16; c = -20;
Δ = b2-4ac
Δ = -162-4·1·(-20)
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{-(-16)-4\sqrt{21}}{2*1}=\frac{16-4\sqrt{21}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{21}}{2*1}=\frac{16+4\sqrt{21}}{2}
$