Substitute #0# for #y#. The roots are the values for #x# when #y# equals #0#. Since the graph is a parabola, there will be two roots.
#-9x^2-22x-55=0# is a quadratic equation in standard form:
#ax^2+bx+c#, where #a=-9#, #b=-22#, #c=-55#.
Quadratic Formula
#x=(-b+-sqrt(b^2-4ac))/(2a)#
Insert the values for #a, b, and c# into the formula.
#x=(-(-22)+sqrt((-22)^2-4*-9*-55))/(2*-9)#
Simplify.
#x=(22+-sqrt(484-1980))/-18#
Simplify.
#x=(22+-sqrt(-1496))/-18#
Prime factorize #-1496#
#x=(22+-sqrt(-1xx2xx2xx2xx11xx17))/-18#
http://www.calculatorsoup.com/calculators/math/prime-factors.php
Simplify.
#x=(22+-isqrt(-1xx2^2xx2xx11xx17))/-18#
Simplify.
#x=(22+-2isqrt(384))/-18#
Simplify. (Divide #22#, #2#, #18# by #2#.)
#x=-(11+isqrt(384))/9,##x=-(11-isqrt(384))/9#
