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2x^2 - 5x - 3 = 0        factor the left side  

(2x + 1) ( x - 3)   = 0      set each factor to 0 and solve for x

2x + 1   = 0  subtract 1 from both sides          x - 3 = 0    add 3 to both sides

2x = -1     divide both sides by 2                      x = 3

x = -1/2 

Answers are in red, NSS