-7x^2+6x+3=0

Question

why are there 2 solutions for this one?
Please and thank you so much

Answer 1

There are two solutions to every quadratic equation.
If you cannot easily see how to factor the expression, then you can always use the quadratic formula. In this case,

x = (-6±√(36+84))/-14 = (3±√30)/7

Answer 2

to find the nature of the roots (solutions)

you can solve it with the quadratic formula (or factoring)

or ... find the discriminant ... b^2 - 4 a c

Answer 3

There are 2 solutions because a graph of the function crosses the x-axis
twice.