Answer
a) 2 real solutions
b) 2 real solutions (look at "work step by step" for explanation)
Work Step by Step
a) We can find how many real number solutions there are based on the discriminant. First, we must write the equation in standard form
$6x^2-5x-7=0$
Then, we find the discriminant.
$D =25 - (4)(6)(-7)$
The value of the discriminant is $193$. Because it is positive, there are 2 real solutions.
b) If $a$ is positive and $c$ is negative, then $-4ac$ will be positive. $b^2$ must be positive because we are dealing with real numbers and squares are always positive. Therefore, $b^2-4ac$ (the discriminant) can be rearranged as $b^2 + (-4ac)$. We don't know the values of the terms, but we know they are positive.
$Positive + Positive = Positive$
Therefore, since the discriminant is positive, there are 2 real solutions.
