https://file.aiquickdraw.com/mathbot/file/1726378661093zzseib9x.jpg

The equation in the image is:

\[
30 = 15x^2 + 15x^2 + 3 + 3
\]

Simplifying the right-hand side:

\[
30 = 30x^2 + 6
\]

Now, solve for \(x^2\):

1. Subtract 6 from both sides:
\[
30 - 6 = 30x^2
\]
\[
24 = 30x^2
\]

2. Divide both sides by 30:
\[
x^2 = \frac{24}{30} = \frac{4}{5}
\]

3. Take the square root of both sides:
\[
x = \pm \sqrt{\frac{4}{5}} = \pm \frac{2}{\sqrt{5}} = \pm \frac{2\sqrt{5}}{5}
\]

Thus, the solution for \(x\) is:
\[
x = \pm \frac{2\sqrt{5}}{5}
\]

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

### Related Questions:
1. How do you simplify quadratic equations like this one?
2. What does it mean to take the square root of a fraction?
3. Can quadratic equations always be solved by factoring?
4. How does the discriminant help in determining the nature of solutions for quadratics?
5. What is the importance of understanding rationalizing the denominator in expressions?

### Tip:
When solving quadratic equations, always check if factoring or the quadratic formula is more suitable to avoid calculation mistakes.

Explore how to solve the quadratic equation from simplifying terms to isolating x. Learn the process of subtracting constants, dividing by the coefficient of x^2, and finding the square roots of fractions, suitable for high school students.

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