# How do you find the discriminant and how many and what type of solutions does 3x^2= -13x - 5 have?

Apr 29, 2015

Rewrite the given expression in standard form
$3 {x}^{2} = - 13 x - 5$
$\rightarrow 3 {x}^{2} + 13 x + 5 = 0$

The discriminant is
$\Delta = {b}^{2} - 4 a c$
and for the given equation, has the value
$\Delta = {13}^{2} - 4 \left(3\right) \left(5\right) = 169 - 60 = 109$

$\Delta > 0$
(but 109 is not a perfect square)
so this equation has
2 Real solutions.