The given equation is:

\[ 3x - 2x^2 = 7 \]

To convert this into standard form \( ax^2 + bx + c = 0 \), we need to move all terms to one side of the equation. Let's rearrange it:

\[ -2x^2 + 3x - 7 = 0 \]

So, the standard form of the quadratic equation is:

\[ -2x^2 + 3x - 7 = 0 \]

Here are the coefficients:
- \( a = -2 \)
- \( b = 3 \)
- \( c = -7 \)

If you have any questions or need further details, feel free to ask.

### Related Questions:
1. How do you determine the standard form of a quadratic equation from its factored form?
2. Why is it important to express quadratic equations in standard form?
3. What methods can be used to solve quadratic equations once in standard form?
4. How do the coefficients \( a \), \( b \), and \( c \) influence the graph of a quadratic equation?
5. Can you show the process of completing the square for one of these equations?
6. How would you use the quadratic formula to solve these equations?
7. What are the possible numbers of real roots for a quadratic equation and how are they determined?
8. How do you derive the quadratic formula from the standard form of a quadratic equation?

### Tip:
When converting equations to standard form, ensure all terms are on one side of the equation and combine like terms if necessary. This makes it easier to identify the coefficients \( a \), \( b \), and \( c \).

Learn how to solve the quadratic equation 3x - 2x^2 = 7 with a detailed step-by-step solution. This problem covers key algebraic concepts, including converting to standard form and identifying coefficients. Suitable for students in Grades 9-12.

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