#x^2 = -13x - 4#
Subtract #-13x - 4# from both sides:
#x^2 + 13x + 4 = 0#
Since it doesn't neatly factor, one of the simplest ways to calculate it is the quadratic formula:
#x = (-b+-sqrt(b^2-4ac))/(2a)# where #a# is the coefficient of #x^2#, #b# is the coefficient of #x#, #c# is the constant.
Substitute the values for #a (1)#, #b (13)#, and# c (4)#...
#x = (-(13)+-sqrt((13)^2-4(1)(4)))/(2(1))#
#x = (-13+-sqrt(153))/2#
#sqrt(153)# can also be represented as #3*sqrt(17)# (because
#sqrt(153) = sqrt(9 * 17) = sqrt(3^2 * 17)#), so it could also be shown as
#x = (-13+-3sqrt(17))/2#