Question

3x^2 - 4x = -2
Solve

Answer 1

`x = \bigg \{( 2 - √(2) \: i )/(3), \: \: ( 2 + √(2) \: i )/(3) \bigg \}`

Explanation:

`3 {x}^(2) - 4x = - 2 \\ 3 {x}^(2) - 4x + 2 = 0 \\ equating \: it \: with \\ a {x}^(2) + bx + c = 0 \\ a = 3 \: \: b = - 4 \: \: c = 2 \\ {b}^(2) - 4ac \\ = {( - 4)}^(2) - 4 * 3 * 2 \\ = 16 - 24 \\ = - 8 \\ \ {b}^(2) - 4ac < 0 \\ \therefore \: given \: quadratic \: equation \: have \: \\ imaginary \: solutios. \\ \\ x = \frac{ - b \pm \sqrt{{b}^(2) - 4ac } }{2a} \\ = ( - ( - 4) \pm √( - 8) )/(2 * 3) \\ = ( 4 \pm 2√(2) \: i )/(2 * 3) \\ = ( 2 \pm √(2) \: i )/(3) \\ \therefore \: x = ( 2 - √(2) \: i )/(3) \: or \: x = ( 2 + √(2) \: i )/(3) \: \\ \\ x = \bigg \{( 2 - √(2) \: i )/(3), \: \: ( 2 + √(2) \: i )/(3) \bigg \}`