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

15x^{2} – 28 = x

Given: 15x^{2} – 28 = x

15x^{2} – x – 28 = 0

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

a = 15, b = – 1, c = – 28

Discriminant D = b^{2} – 4ac

= (– 1)^{2} – 4.15. – 28

= 1 + 1680 = 1681 > 0

Hence the roots of equation are real.

Roots are given by

Hence the roots of equation are

7