The quadratic equation 5x^2 + 13x +8 =0 has to be solved.

The solution of quadratic equation ax^2 + bx + c = 0 is given by the formula `(-b+-sqrt(b^2 - 4ac))/(2a)`

For 5x^2 + 13x +8 =0, a = 5, b = 13 and c = 8. Substituting these values in the formula for the roots gives:

`(-13+-sqrt(13^2 - 4*5*8))/(2*5)`

= `(-13+-sqrt(169 - 160))/(2*5)`

= `(-13+-sqrt(9))/(2*5)`

= `(-13 - 3)/10` and `(-13 + 3)/10`

= -1.6 and -1

The roots of the equation are -1 and -1.6

We have to solve the quadratic equation 5x^2+ 13x +8 =0

To do that we can use the direct formula to calculate roots or we use an easier method here.

Now we write 13x as the sum of two factors so that their product is 40 x^2. We can write 13x as 8x + 5x.

=> 5x^2+ 13x +8 =0

=> 5x^2 + 8x + 5 x + 8 =0

=> x ( 5x +8) +1 (5x+8) =0

=> (x+1)(5x+8) =0

=> (x + 1) =0 or (5x+8) =0

=> x -1 or x = -8/5

**So the roots of the quadratic equation are -1 and -8/5**