 42400 \times  (3157,895-2,579x)-16,8 \times  (3157,895-2,579x)x-72000x =  84000000 

Let's solve the given equation step by step:

\[
42400 \times (3157.895 - 2.579x) - 16.8 \times (3157.895 - 2.579x)x - 72000x = 84000000
\]

### Step 1: Distribute the constants
Distribute \( 42400 \) and \( -16.8x \) across their respective terms:

\[
42400 \times (3157.895 - 2.579x) = 42400 \times 3157.895 - 42400 \times 2.579x
\]
\[
16.8x \times (3157.895 - 2.579x) = 16.8x \times 3157.895 - 16.8x \times 2.579x
\]

Calculating the individual terms:
\[
42400 \times 3157.895 = 133895728
\]
\[
42400 \times 2.579x = 109661.6x
\]
\[
16.8x \times 3157.895 = 53012.596x
\]
\[
16.8x \times 2.579x = 43.3272x^2
\]

Now, the equation becomes:
\[
133895728 - 109661.6x - 53012.596x - 43.3272x^2 - 72000x = 84000000
\]

### Step 2: Combine like terms
Let's combine all the terms involving \( x \):
\[
-109661.6x - 53012.596x - 72000x = -234674.196x
\]

So the equation is now:
\[
133895728 - 234674.196x - 43.3272x^2 = 84000000
\]

### Step 3: Move the constant term to the other side
Subtract \( 84000000 \) from both sides:
\[
133895728 - 84000000 - 234674.196x - 43.3272x^2 = 0
\]
\[
49895728 - 234674.196x - 43.3272x^2 = 0
\]

### Step 4: Rearrange the equation
\[
43.3272x^2 + 234674.196x - 49895728 = 0
\]

### Step 5: Solve using the quadratic formula
The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
where:
- \( a = 43.3272 \)
- \( b = 234674.196 \)
- \( c = -49895728 \)

Let me now calculate the discriminant and the solution.The solutions to the quadratic equation are:

\[
x_1 = 204.87 \quad \text{and} \quad x_2 = -5621.19
\]

Thus, the two possible values for \( x \) are approximately 204.87 and -5621.19.

Do you have any questions, or would you like further details on the steps?

Here are 5 related questions you might find helpful:
1. How does the quadratic formula work in detail?
2. What are the conditions for a quadratic equation to have real solutions?
3. How does the discriminant affect the nature of the solutions?
4. Can this equation be solved using other methods, like factoring or completing the square?
5. How can the quadratic formula be applied in practical scenarios?

**Tip:** When solving quadratic equations, always check the discriminant first to determine the nature of the roots (real or complex).

42400 × (3157.895 - 2.579x) - 16.8 × (3157.895 - 2.579x)x - 72000x = 84000000

This guide walks you through solving the quadratic equation 42400 × (3157.895 - 2.579x) - 16.8 × (3157.895 - 2.579x)x - 72000x = 84000000. Learn how to distribute constants, combine like terms, and apply the quadratic formula for solutions. Suitable for advanced algebra students in Grades 10-12.

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