Question

How do you use the quadratic formula to solve `3x^2-2x+7=0`?

Answer 1

Our equation is of the form `ax^2+bx+c=0`, therefore, we can use the quadratic formula. The quadratic formula is `x = (-b +- sqrt(D))/(2a)`, with `D = b^2-4ac`. We see that `a=3, b=-2` and `c=7`.

Firstly, we calculate `D`.
`D = b^2-4ac = (-2)^2-4*3*7 = -80`. Because D is less than zero, there are no real roots. We can however calculate the imaginary solutions. We just calculate `x`:
`x = (-b +- sqrt(D))/(2a) = (2+-sqrt(-80))/(2*3) = (2+-sqrt(-1)*sqrt(16)*sqrt(5))/6 = (2+-i*4sqrt(5))/6 = 1/3+- 2/3 isqrt(5)`