To solve the equation \(2x^2 - 3 = 15\), we need to isolate \(x\). Here's the step-by-step process:

1. **Add 3 to both sides** to eliminate the \(-3\) on the left side:

\[
2x^2 - 3 + 3 = 15 + 3
\]

\[
2x^2 = 18
\]

2. **Divide both sides by 2** to solve for \(x^2\):

\[
\frac{2x^2}{2} = \frac{18}{2}
\]

\[
x^2 = 9
\]

3. **Take the square root of both sides** to solve for \(x\). Remember to consider both the positive and negative roots:

\[
x = \pm\sqrt{9}
\]

\[
x = \pm 3
\]

### Solution

The solutions to the equation \(2x^2 - 3 = 15\) are:

\[
x = 3 \quad \text{and} \quad x = -3
\]

Would you like more details, or do you have any questions?

Here are some related questions that you might find interesting:

1. How would the solutions change if the equation was \(2x^2 - 3 = 0\)?
2. What if the equation was \(2x^2 - 3 = -15\)?
3. How can we solve \(2x^2 - 3 = 15\) graphically?
4. What are the properties of quadratic equations like \(ax^2 + bx + c = 0\)?
5. How do we solve quadratic equations using the quadratic formula?

**Tip:** Always consider both the positive and negative square roots when solving equations involving squares.

Learn how to solve the quadratic equation 2x^2 - 3 = 15 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic equation formula and the quadratic formula theorem. Suitable for students in Grades 7-9.

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