Question

Solve this quadratic Equation 3x^2 + 4x = 2

Answer 1

we know that for

`a{x}^(2) + bx + c = 0`

the roots are:

`x1 = \frac{ - b + \sqrt{ { {b}^(2) } - 4ac} }{2a}`

and

`x2 = \frac{ - b - \sqrt{ { {b}^(2) } - 4ac} }{2a}`

so putting into the formula we get:

`3 {x}^(2) + 4x - 2 = 0`

and

`{{b}^(2) } - 4ac = {4}^(2) - 4 * 3 * ( - 2) = \\ 16 + 24 = 40`

so:

`x1 = ( - 4 + √(40) )/(2 * 3) = ( - 2 + √(10) )/(3)`

and

`x2 = ( - 4 - √(40) )/(2 * 3) = ( - 2 - √(10))/(3)`