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

May 12, 2015

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

$- 3 {x}^{2} + 7 x - 2 < 0$

$\Delta = {7}^{2} - 4 \cdot \left(- 3\right) \cdot \left(- 2\right) = 25$
$\sqrt{\Delta} = 5$
${x}_{1} = \frac{- 7 - 5}{-} 6 = 2$
${x}_{2} = \frac{- 7 + 5}{-} 6 = \frac{1}{3}$
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)