Solution
Five times a positive integer is 3 less than twice its square.
$$2I^2 -5I =3$$
this forms a quadratic equation
lcm of 3 and 2 = 6
$$2I^2 -5I -3$$
$$2I^2 -6I+I-3 $$ (middle term factorization)
$$2I(I-3)+1(I-3)$$
I =3 , I = $$\frac{-1}{2}$$
integer must be positive so I =3
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