The given quadratic equation is 2x^2 - 5x - 8 = 0

We cannot find the factors here. Use the quadratic equation which gives the roots as:

x1 = [-b + sqrt (b^2 - 4ac)]/2a and x2 = [-b - sqrt (b^2 - 4ac)]/2a

For the given equation 2x^2 - 5x - 8 = 0,

x1 = 5/4 + sqrt (25 + 64) / 4

=> 5/4 + sqrt 89 / 4

x2 = 5/4 - sqrt 89 / 4

**The solutions of the equation are 5/4 + (sqrt 89) / 4 and 5/4 - (sqrt 89) / 4**

Given the quadratic equation 2x^2 -5x -8 = 0

We will use the quadratic formula to find the roots.

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

We will substitute:

==> a = 2 b= -5 c= -8

==> x1= ( 5+sqrt( 25-4*2*-8) / 2*2

= (5+ sqrt(89) / 4

==> x2= ( 5-sqrt(89)/4

Then the real solutions for the function are:

**x = { (5+sqrt89)/4 , (5-sqrt89)/4 }**

2x^2 -5x -8 = 0

a=2 b=-5 c=-8

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

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

`(5+-sqrt(25+64))/ (4) `

`(5+-sqrt(89))/ (4) `

`x=(5+sqrt(89))/ (4) `

`x=(5-sqrt(89))/ (4) `