For the equation given below, find the value of 'm' so that the equation has equal roots. Also, find the solution of the equation :

(m - 3)x² - 4x + 1 = 0

Since, equation has equal roots, D = 0.

∴ b² - 4ac = 0

⇒ (-4)² - 4(m - 3)(1) = 0

⇒ 16 - 4m + 12 = 0

⇒ 4m = 28

⇒ m = 7.

Substituting m = 7 in (m - 3)x² - 4x + 1 = 0 we get,

⇒ (7 - 3)x² - 4x + 1 = 0

⇒ 4x² - 4x + 1 = 0

⇒ 4x² - 2x - 2x + 1 = 0

⇒ 2x(2x - 1) - 1(2x - 1) = 0

⇒ (2x - 1)(2x - 1) = 0

⇒ (2x - 1) = 0 or (2x - 1) = 0

⇒ x = $\dfrac{1}{2}$.

Hence, m = 7 and x = $\dfrac{1}{2}$.