How do you solve #6n^2-19n+15=0#?

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Answer 1 · 2016-05-19T15:37:56

The solutions for the expression are:
# n = 5/3#

# n = 3/2#

#6n^2 - 19n + 15 = 0 #

The equation is of the form #color(blue)(an^2+bn+c=0# where:
#a=6, b=-19, c=15#

The Discriminant is given by:
#Delta=b^2-4*a*c#

# = (-19)^2-(4* 6 * 15)#

# = 361 - 360= 1#

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

#n = (-(-19)+-sqrt(1))/(2*6) = (19+-1)/12#

# n = (19+1) /12 = 20/12 = 5/3#

# n = (19-1) /12 = 18/12 = 3/2#