Hi,
x^2+4x-77=0
factoring
(x + 11)(x-7) = 0 |using the principle of zero products
( x + 11)= 0 x = -11
(x-7) = 0 x = 7
May check your factoring using the FOIL Method
(x + 11)(x-7) = 0
F First terms x^2
O Outside terms -7x
I Inside terms 11x
L Last terms -77