Question

How do you solve `7x^2 + 8x + 5 = 0` using the quadratic formula?

Answer 1

`x= (-8+-2sqrt(-19))/14`

Explanation:

The quadratic formula states that the solutions to a quadratic of the form `ax^2 +bx+c = 0` are given by

`x =( -b+-sqrt(b^2-4ac))/(2a)`

So in this case

`x = (-8+-sqrt(8^2-4*7*5))/(2*7)`

`=(-8+-sqrt(64-140))/14 = (-8+-sqrt(-76))/14 = (-8+-2sqrt(-19))/14`

This has only imaginary solutions.