Since this can't be solved using ordinary factoring then use the quadratic formula given as:
[tex]x = \frac{-b (+-) \sqrt{b^2 - 4ac} }{2a} [/tex]
2x² - 5x - 3 = -4
2x² - 5x - 3 + 4 = 0
2x² - 5x + 1 = 0
substituting the values to the quadratic formula you'll have:
[tex]x = \frac{ -(-5) (+-) \sqrt{(-5)^2-4(2)(1)} }{2(2)}[/tex]
[tex]x_1 = \frac{5 + \sqrt{17} }{4} [/tex]
[tex]x_2 = \frac{5- \sqrt{17} }{4} [/tex]
