How do you solve the quadratic using the quadratic formula given 7-8z^2=6z+16 over the set of complex numbers?

1 Answer
Nov 20, 2016

The solution is S={(-3+3isqrt7)/(8),(-3-3isqrt7)/(8)}

Explanation:

Rearranging the equation

8z^2+6z+9=0

Let's calculate the discriminant

Delta=b^2-4ac=36-4*8*9=36-288=-252

Delta<0, so solutions are in CC

Then,
z=(-b+-sqrtDelta)/(2a)=(-6+-isqrt252)/16

=(-6+-6isqrt7)/16=(-3+-3isqrt7)/(8)