Question

How do you use the quadratic formula to solve for the roots in the following equation `4x^2+5x+2=2x^2+7x-1`?

Answer 1

`x=(1+2i)/2` or `(1-2i)/2`

Explanation:

`->4x^2-2x^2+5x-7x+2-(-1)=0`
`->2x^2-2x+3=0`

And then you use the quadratic formula `x=(-b+-sqrt(b^2-4ac))/(2a)` for the equation `ax^2+bx+c=0`

and here we have got `a=2`, `b=-2` and `c=3`

hence `x=(-(-2)+-sqrt((-2)^2-4xx2xx3))/(2xx2)`

= `(2+-sqrt(-16))/4=(2+-4i)/4`

i.e. `x=(1+2i)/2` or `(1-2i)/2`