Question

How do you solve `2x^2 - 3x + 4 = 0`?

Answer 1

This is a quadratic equation of the form:
`ax^2+bx+c=0`
Where:
`a=2`
`b=-3`
`c=4`
So you can use the Quadratic Formula:
`x_(1,2)=(-b+-sqrt(b^2-4ac))/(2a)`
`=(3+-sqrt(9-32))/4`
The negative argument of the square root tells you that you will not get Real solutions (you'll get Complex Solutions).
`x_(1,2)=(3+-sqrt(-1*23))/4=(3+-isqrt(23))/4`
Where `i=sqrt(-1)`