Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

16x^{2} = 24x + 1

Given: 16x^{2} = 24x + 1

16x^{2} – 24x – 1 = 0

Comparing with standard quadratic equation ax^{2} + bx + c = 0

a = 16, b = – 24, c = – 1

Discriminant D = b^{2} – 4ac

= (– 24)^{2} – 4.16. – 1

= 576 + 64 = 640 > 0

Hence the roots of equation are real.

Roots are given by

Hence the roots of equation are

6