We have the quadratic equation 3x^2 -5x -4 = 0.

The roots of the equation are

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

=> [ 5 + sqrt ( 25 + 48)]/ 6

=> 5/6 + sqrt 73 / 6

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

=> [ 5 - sqrt ( 25 + 48)]/ 6

=> 5/6 - sqrt 73 / 6

**Therefore the roots are 5/6 + sqrt 73 / 6 and 5/6 - sqrt 73 / 6.**

Given the quadratic equation:

3x^2 - 5x - 4 = 0

==> a = 3 b= -5 c = -4

We need to solve for x using the quadratic formula.

We know that:

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

==> x1= ( 5 + sqrt(25+4*3*4) /2*3

= (5 + sqrt(73) / 6

**==> x1= (5+sqrt73)/6**

**==> x2= (5-sqrt73)/6**

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