Solve Quadratic equations 2x² - x - 15 = x(x + 1)

Solution:

Given: 2x² - x - 15 = x(x + 1)

Rewriting the quadratic equation in the standard form, we get

2x² - x - 15 = x² + x

x² - 2x - 15 = 0-------> (1)

Factorizing the quadratic equation, we get

x² - 5x + 3x - 15 = 0

x(x - 5) + 3(x - 5) = 0

(x + 3)(x - 5) = 0

When (x + 3)= 0 ⇒ x = -3

When (x - 5) = 0 ⇒ x = 5

Solve Quadratic equations 2x² - x - 15 = x(x + 1)

Summary:

The roots of the given equation 2x² - x - 15 = x(x + 1) are -3 and 5.