x^2-4X-5=0

Δ=16+20=36<=>Δ=6

X 1= 4 + 6 div 2=5<=> X1=5

X 2 = 4-6div 2= -1 <=> X2=-1

x^2 - 4x - 5  = 0        factor the trinomial

(x - 5) ( x + 1)  = 0

Set both linear factors to 0  and solve for x  

x - 5  = 0                         or              x + 1  = 0

add 5 to both sides                          subtract 1 from each side

x = 5                                                 x = -1

And those are the solutions