Question

Determine the number and type of solutions for 5x2 + 1x + 7 = 0.

1 Rational Double

2 Irrational

2 Rational

2 Complex

Answer 1

You'll have to use that discriminant I gave ya. And this link is helpful:
http://www.mathwarehouse.com/quadratic/discriminant-in-quadratic-equation.php
Particularly the first half.

Answer 2

5x^2 + x + 7 = 0
The Discriminant D = b^2 - 4ac = 1 - 140 = - 139 < 0
There are 2 complex roots.