Answer:
[tex] x = \dfrac{1}{5} \pm \dfrac{\sqrt{46}}{5} [/tex]
Step-by-step explanation:
5x^2 - 2x - 9 = 0
a = 5; b = -2; c = -9
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4(5)(-9)}}{2(5)} [/tex]
[tex] x = \dfrac{2 \pm \sqrt{4 + 180}}{10} [/tex]
[tex] x = \dfrac{2 \pm \sqrt{184}}{10} [/tex]
[tex] x = \dfrac{2 \pm \sqrt{4 \times 46}}{10} [/tex]
[tex] x = \dfrac{2 \pm 2\sqrt{46}}{10} [/tex]
[tex] x = \dfrac{1 \pm \sqrt{46}}{5} [/tex]
[tex] x = \dfrac{1}{5} \pm \dfrac{\sqrt{46}}{5} [/tex]
