Step 1

We know that, for a standard form of quadratic \(ax^{2}+bx+c=0\), the value of discriminant D is calculated as

\(D=b^{2}-4ac\)...(1)

Now,

If \(D>0\), then both the roots of the equation must be real and distinct.

If \(D=0\), then both the roots must be real and equal.

If \(D<0\), then both the roots must be imaginary.

Step 2

We have the given quadratic equation as

\(7x^{2}-2x-14=0\)...(2)

On comparing the equation (2) with standard equation \(ax^{2}+bx+c=0\), we get the result as

\(a=7, b=−2\) and \(c=−14\)

On using equation (1), we get the discriminant of equation \(7x^{2}−2x−14=0\) as

\(D=(-2)^{2}-(4)(7)(-14)\)

\(D=4+392\)

\(D=396\)

\(D>0\)

Hence, there will be two real and distinct solution.