Question

How do you solve `-2 + 7x - 3x^2<0`?

Answer 1

The answer is `x in (-oo;1/3)uu(2;+oo)`

`-3x^2+7x-2<0`

`Delta=7^2-4*(-3)*(-2)=25`
`sqrt(Delta)=5`
`x_1=(-7-5)/-6=2`
`x_2=(-7+5)/-6=1/3`
graph{-3x^2+7x-2 [-4.385, 4.386, -2.19, 2.194]}

From the graph you see,that the solution of the inequality is:
`f(x)<0 iff x in (-oo;1/3) uu (2; +oo)`