Determine the LCD of the given equation. Then, transform it to the general form of quadratic equation.

5
x
+
x
−
3
4
=
2
x
5
​
+
4
x−3
​
=2

The given equation is:

\[
\frac{5}{x} + \frac{x - 3}{4} = 2
\]

### Step 1: Determine the Least Common Denominator (LCD)

The denominators in this equation are \( x \) and 4. The LCD is the product of these denominators:

\[
\text{LCD} = 4x
\]

### Step 2: Multiply the Entire Equation by the LCD

Multiplying each term by \( 4x \) gives:

\[
4x \cdot \frac{5}{x} + 4x \cdot \frac{x - 3}{4} = 4x \cdot 2
\]

This simplifies to:

\[
4 \cdot 5 + x(x - 3) = 8x
\]

### Step 3: Expand and Simplify the Equation

Expanding \( x(x - 3) \) gives:

\[
20 + x^2 - 3x = 8x
\]

### Step 4: Transform the Equation into General Quadratic Form

To get the equation into the standard quadratic form \( ax^2 + bx + c = 0 \), subtract \( 8x \) from both sides:

\[
x^2 - 3x - 8x + 20 = 0
\]

This simplifies to:

\[
x^2 - 11x + 20 = 0
\]

### Final Answer

The equation in general quadratic form is:

\[
x^2 - 11x + 20 = 0
\]

---

Do you need more details or have any questions? Here are some related questions you might find interesting:

1. How do you find the roots of the quadratic equation \( x^2 - 11x + 20 = 0 \)?
2. What are the methods to solve a quadratic equation?
3. How do you determine if a quadratic equation has real or complex roots?
4. How can you apply the quadratic formula to solve \( x^2 - 11x + 20 = 0 \)?
5. What is the discriminant of a quadratic equation, and how does it relate to the nature of the roots?

**Tip:** Always check if a quadratic equation can be factored easily before applying the quadratic formula!

Learn how to transform and solve the equation 5/x + (x - 3)/4 = 2x step-by-step. This problem involves understanding quadratic equations and their transformations. Suitable for high school students and learners interested in algebraic problem-solving.

Math Problem Statement

5 x + x − 3 4

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