How do you solve #2x² + 10 = 9x#?

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Answer 1 · 2016-04-10T16:44:42

The solutions are:
#x = 2#

#x = 5/2#

#2x^2 + 10 = 9x#

#2x^2 -9x + 10 = 0#

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

#a= 2 , b=- 9 , c= 10#

The Discriminant is given by:
#Delta=b^2-4*a*c#
# = (-9)^2-(4 * 2 * 10)#
# = 81 - 80 = 1 #

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

#x = (-(-9)+-sqrt(1))/(2 * 2 ) = (9+-1)/ 4#

#x = (9 - 1 ) / 4 = 8/4 = 2#

#x = (9 + 1 ) / 4 = 10/4 = 5/2#