a)
[tex]-2x^{2}+5x-3 = 0\\\\a = -2. \ b = 5, \ c = -3\\\\\Delta = b^{2}-4ac = 5^{2}-4\cdot(-2)\cdot(-3) = 25 - 24 = 1\\\\\sqrt{\Delta} = \sqrt{1} = 1\\\\x_1 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-5+1}{2\cdot(-2)} = \frac{-4}{-4} = 1\\\\x_2 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-5-1}{-4} = \frac{-6}{-4} = \frac{3}{4} = 1\frac{1}{2}\\\\\boxed{x \in \{1, 1\frac{1}{2}\}}[/tex]
b)
[tex]4x^{2}+12x+9 = 0\\\\(2x+3)^{2} = 0\\\\2x+3 = 0\\\\2x = -3 \ \ \ |:2\\\\x = -\frac{3}{2}\\\\\boxed{x = -1\frac{1}{2}}[/tex]
