Question

Solve –2x2 +3x – 9 = 0

Answer 1

use quadratic formula

\[x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

first you can multiply both sides by -1, and you get
\[2x^2 - 3x + 9 = 0\]

so
a = 2
b = -3
c = 9

\[x_{1,2} = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(2)(9)}}{2(2)}\]
\[x_{1,2} = \frac{3 \pm \sqrt{9 - 72}}{4}\]
\[x_{1,2} = \frac{3 \pm \sqrt{-63}}{4}\]
\[x_{1,2} = \frac{3 \pm i\sqrt{9}\sqrt{7}}{4}\]
\[x_{1,2} = \frac{3 \pm 3i\sqrt{7}}{4}\]

therefore

\[x_{1} = \frac{3}{4} + \frac{3\sqrt{7}}{4}i\]
\[x_{2} = \frac{3}{4} - \frac{3\sqrt{7}}{4}i\]