The sum of the roots of the equation 1/2x^2-5/4x-3=0

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