# How do you describe the nature of the roots of the equation 3x^2-4x=-2?

Aug 29, 2016

The roots are imaginary / non-real.
The equation cannot be solved.

#### Explanation:

Work with $3 {x}^{2} - 4 x + 2 = 0$

Find the discriminant. $\Delta = {b}^{2} - 4 a c$

$\Delta = {\left(- 4\right)}^{2} - 4 \left(3\right) \left(2\right)$
$\Delta = 16 - 24$
$\Delta = - 8$

$\Delta < 0$

The roots are imaginary / non-real
(They do not exist, so there are no real solutions to this equation).