Question

How many, and what type of, solutions does 6x^2−2x+7=0 have?

2 nonreal solutions1 rational solution2 rational solutions2 irrational solutions

Answer 1

You can use the discriminant to solve this problem.

$b^{2} -4ac$ where a=6, b=-2, c=7
Plug it in
$(-2)^{2} -4(6)(7)$
4-168=-164

Since it is negative there are no real solutions.