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Let's solve the given quadratic equation step by step.

We start with the equation:
\[
8x^2 - 5x + 87 = 7x^2 + 5x
\]

### Step 1: Rearrange the equation to set it equal to zero.
Move all terms to one side:
\[
8x^2 - 5x + 87 - 7x^2 - 5x = 0
\]

Simplify:
\[
(8x^2 - 7x^2) + (-5x - 5x) + 87 = 0
\]
\[
x^2 - 10x + 87 = 0
\]

### Step 2: Identify the coefficients of the quadratic equation.
The standard form of a quadratic equation is:
\[
ax^2 + bx + c = 0
\]
From the equation \(x^2 - 10x + 87 = 0\), we can identify:
- \(a = 1\)
- \(b = -10\)
- \(c = 87\)

### Step 3: Calculate the discriminant.
The discriminant \(\Delta\) of a quadratic equation is given by:
\[
\Delta = b^2 - 4ac
\]
Substitute the values of \(a\), \(b\), and \(c\):
\[
\Delta = (-10)^2 - 4(1)(87)
\]
\[
\Delta = 100 - 348
\]
\[
\Delta = -248
\]

### Conclusion:
The discriminant of the quadratic equation is \(-248\).

This negative discriminant indicates that the quadratic equation has two complex (non-real) solutions.

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Would you like any further explanation on this, or have any questions? Here are a few related questions you might find helpful:

1. How can you determine the nature of the roots from the discriminant?
2. What happens when the discriminant is zero?
3. How do you solve a quadratic equation when the discriminant is negative?
4. What is the geometric interpretation of a quadratic with a negative discriminant?
5. How can you factor a quadratic equation when the discriminant is positive?

**Tip**: A negative discriminant always implies that the quadratic equation has complex conjugate roots.

For the following quadratic equation, find the discriminant: 8x^2 - 5x + 87 = 7x^2 + 5x.

Learn how to find the discriminant of the quadratic equation 8x^2 - 5x + 87 = 7x^2 + 5x. This problem involves rearranging the equation, identifying coefficients, and using the discriminant formula to determine the nature of the roots. Suitable for students in Grades 8-10.

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