Mathematics

Solve the following equation:
x(2x + 5) = 3

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Given, x(2x + 5) = 3.

⇒ 2x² + 5x = 3

⇒ 2x² + 5x - 3 = 0

⇒ 2x² + 6x - x - 3 = 0

⇒ 2x(x + 3) - 1(x + 3) = 0

⇒ (2x - 1)(x + 3) = 0

⇒ 2x - 1 = 0 or x + 3 = 0

⇒ 2x = 1 or x = -3

⇒ x = $\dfrac{1}{2}$ or x = -3.

Hence, roots of the given equations are -3, $\dfrac{1}{2}$

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