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find all the real solutions of the equation

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2 Answers

2x²+3x+5=0 has solutions by the quadratic formula x=(-3±√(9-4×2×5))/4 =(-3±√(-31))/4
There are no real solutions, since the discriminant is -31, whose square root is imaginary.

b^2 - 4ac = 9 - 4(2)(5) = 9 - 40 = -31

Since the discriminant is negative, the quadratic equation has no real values for its solution. It only has imaginary solutions.