The equation is 1/2x² -5/4x -3=0
Multiplying all the terms by 4 to remove fractions
2x²-5x-12=0
we can use factorization method;
product = -24
sum = -5
numbers= -8 and 3
Threfore; 2x²-8x+3x-12 =0
2x(x-4) +3(x-4) =0
= (2x+3)(x-4) =0
thus 2x +3= 0 or x-4 =0
therefore; x = -3/2 and x =4
Thus the sum of the roots will be (-3/2 +4) = 2.5