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2x^2+5x-3 <=0

(2x-1)(2x+3)<=0

divide the numerical axis in to (-inf, -3), (-3,1/2), (1/2, inf), then in both (-inf, -3), and (1/2, inf) , 2x^2+5x-3 >0, since the parabola y=2x^2+5x-3 is open up, thus the solution is

[-3,1/2]

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