Question 164917
Find b^2 – 4ac and the number of real solutions to each equation.
9m^2+16=24m
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First, convert your equation into the form of:
am^2 + bm + c = 0
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Starting with:
9m^2+16=24m
subtracting 24m from both sides:
9m^2-24m+16=0
we "see" that:
a = 9
b = -24
c = 16
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b^2 – 4ac 
is called the discriminant
if POSITIVE, then TWO real solutions
if ZERO, then ONE real solutions
if NEGATIVE, then TWO complex solutions
.
b^2 – 4ac 
(-24)^2 – 4(9)(16)
576 - 576 = 0
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Since discriminate is ZERO -- 
ONE real solution