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

15x2 – 28 = x

Given: 15x2 – 28 = x

15x2 – x – 28 = 0


Comparing with standard quadratic equation ax2 + bx + c = 0


a = 15, b = – 1, c = – 28


Discriminant D = b2 – 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