m^2-2m-13=6

Solution for m^2-2m-13=6 equation:

m^2-2m-13=6

We move all terms to the left:

m^2-2m-13-(6)=0

We add all the numbers together, and all the variables

m^2-2m-19=0

a = 1; b = -2; c = -19;
Δ = b2-4ac
Δ = -22-4·1·(-19)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{5}}{2*1}=\frac{2-4\sqrt{5}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{5}}{2*1}=\frac{2+4\sqrt{5}}{2}
$