Question

How do you find the solutions of `-5+2x^2=-6x`?

Answer 1

`(3 +- sqrt19)/2`

Explanation:

`-5+2x^2=-6x`
`hArr2x^2 + 6x - 5 = 0`
Solve this quadratic equation by the improved quadratic formula.
`D = d^2 = b^2 - 4ac = 36 + 40 = 76` --> `d = +- 2sqrt19`
There are 2 real roots:
`x = -b/(2a) +- d/(2a) = - 6/4 +- (2sqrt19)/4 = (3 +- sqrt19)/2`
`x1 = (3 + sqrt19)/2`
`x2 = (3 - sqrt19)/2`