SOLUTION: solve this equation: 2x^2+3x+19=0

Question 845343: solve this equation:
2x^2+3x+19=0
Answer by pmesler(52) (Show Source): You can put this solution on YOUR website!
This is a simple quadratic equation. To solve this you simply use the quadratic formula

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -143 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -143 is + or - .

The solution is

Here's your graph:

The roots are complex because the discriminant is negative. Anytime you have a negative square root, you have an imaginary number. A complex number is a real number plus an imaginary number of the form
a+-bi where a and b are real and i is the imaginary unit sqrt(-1).
In this case the roots are -3+11.95i/4 and -3-11.95i/4.
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