Question

Solve the following equation by using formula :

(2x + 3)(3x – 2) + 2 = 0

Answer 1

(2x + 3)(3x – 2) + 2 = 0
6x² - 4x + 9x - 6 + 2 = 0
6x² + 5x - 4 = 0
Here a = 6, b = 5, c = -4
D = b² - 4ac
= (5)² - 4 x 6 x (-4)
= 25 + 96
= 121

∵ x = ${\displaystyle \frac{-b+\sqrt{\text{D}}}{2a}}$

= ${\displaystyle \frac{-5\pm \sqrt{121}}{5\times 6}}$

= ${\displaystyle \frac{-5\pm 11}{12}}$

∴ x₁ = ${\displaystyle \frac{-5+11}{12}}$

= ${\displaystyle \frac{6}{12}}$

= ${\displaystyle \frac{1}{2}}$

∴ x₂ = ${\displaystyle \frac{-5-11}{12}}$

= ${\displaystyle \frac{-16}{12}}$

= ${\displaystyle \frac{-4}{3}}$

Hence x = ${\displaystyle \frac{1}{2},\frac{-4}{3}}$.