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

1 Answer
Feb 4, 2015

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)#