How do you solve #3p^2 + 17p= -10#?

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Answer 1 · 2016-03-18T15:02:52

The solutions are:
#p=-2/3#

#p=-5#

#3p^2 + 17p = -10#

#3p^2 + 17p +10=0#

The equation is of the form #color(blue)(ap^2+bp+c=0# where:

#a=3, b=17, c=10#

The Discriminant is given by:

#Delta=b^2-4*a*c#

# = (17)^2-(4*3*10)#

# = 289-120= 169 #

The solutions are found using the formula
#p=(-b+-sqrtDelta)/(2*a)#

#p = (-17+-sqrt(169))/(2*3) = ((-17 +-13))/6#

#p=(-17 +13)/6 = -cancel4/cancel6 = -2/3#

#p=(-17 -13)/6 = -30/6 = -5#