Question

Solve
`-2x^2 +3x - 9 = 0`

Answer 1

`x= (3-3√(7)i )/(4)` and
`x= (3+3√(7)i )/(4)`

Explanation:

We have to solve the given equation - 2x² + 3x - 9 = 0

To solve the equation given above we have to factorize the left-hand side of the equation.

But it can not be factorized. So, use the Sridhar Achaya formula.

Therefore,
`x= \frac{-3 + \sqrt{3^(2)-4 * (-2) * (-9) } }{2* (-2)}` and
`x= \frac{-3 -\sqrt{3^(2)-4 * (-2) * (-9) } }{2* (-2)}`

So,
`x= (3-3√(7)i )/(4)` and
`x= (3+3√(7)i )/(4)` {Where
`i=√(-1)`}

Therefore, the solutions are imaginary numbers. (Answer)

Note: The Sridhar Acharya Formula gives if ax² + bx + c = 0, then the roots of the equation are
`x = \frac{-b + \sqrt{b^(2)-4ac } }{2a}` and
`x = \frac{-b - \sqrt{b^(2)-4ac } }{2a}`.