How do you solve #10v² = 13v + 3#?

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Answer 1 · 2016-03-26T14:46:14

The solutions are:
#v = 3/2#

#v = -1 /5#

#10v^2 = 13v +3#

#10v^2 - 13v -3 = 0#

The equation is of the form #color(blue)(av^2+bv+c=0# where:
#a=10 , b=-13, c=-3#

The Discriminant is given by:

#color(green)(Delta=b^2-4*a*c#

# = (-13)^2-(4* 10 * (-3))#

# = 169 + 120 = 289#

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

# v = (-(-13)+-sqrt(289))/(2*10) = (13+-17)/20#

#v = (13+17)/20 = 30 / 20 = 3/2#

#v = (13-17)/20 = -4/ 20 = -1 /5#