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)