How to solve 8x^2+6x+5=0 using the quadratic formula?

Question

I am struggling with this and I feel hopeless.. what are the two solutions? Thanks a ton.

Answer 1

8x^2+6x+5 = 0

Compare it to quadratic formula ax^2+bx+c = 0

Then the roots are [-b±√[b^2-4ac]]/2a

a = 8, b = 6, c =5

x = [-6±√(36-4*8*5)]/2*8

x = [-6±√36-160)]/16

x = [-6±√-124]/16

x = (-6+√-124)/16 and x = (-6-√-124)/16

Squre root negitive is not possible, so it have no real roots.

Given equation have two imaginary roots

Solutions x = -6+124i/16 and x = -6-124i/16.

Comments

Typo mistake in last line of above solution.

Solutions are x = (- 6 + 2i√31)/16 and x = (- 6 - 2i√31)/16.