# What type of solutions and how many solutions does the equation 41x^2-31x-52=0 have?

Nov 12, 2014

$41 {x}^{2} - 31 x - 52 = 0$

$\implies \left\{\begin{matrix}a = 41 \\ b = - 31 \\ c = - 52\end{matrix}\right.$

Let us compute its discriminant.

$D = {b}^{2} - 4 a c = {\left(- 31\right)}^{2} - 4 \left(41\right) \left(- 52\right) = 9489 > 0$,

which indicates that it has two real solutions.

I hope that this was helpful.