Find the real solutions, if any, of the following equation. Use the quadratic formula. $$ 5 x^{2}=6 x $$ Select the correct choice below and, if necessary, fill in the answer box to complete your answer. A. The solution set is $$ \} $$ (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) B. The solution is not a real number.

Question

UpStudy AI · Accepted Answer

To solve the equation $$ 5x^{2} = 6x $$ using the quadratic formula, follow these steps:

1. **Rewrite the Equation in Standard Form:**
   
   Bring all terms to one side to set the equation to zero:
   $$
   5x^{2} - 6x = 0
   $$
   
   This is in the standard quadratic form $$ ax^{2} + bx + c = 0 $$, where:
   $$
   a = 5,\quad b = -6,\quad c = 0
   $$

2. **Apply the Quadratic Formula:**
   
   The quadratic formula is:
   $$
   x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}
   $$
   
   Plugging in the values:
   $$
   x = \frac{-(-6) \pm \sqrt{(-6)^{2} - 4 \cdot 5 \cdot 0}}{2 \cdot 5}
   $$
   $$
   x = \frac{6 \pm \sqrt{36}}{10}
   $$
   $$
   x = \frac{6 \pm 6}{10}
   $$
   
3. **Calculate the Solutions:**
   
   - **First Solution:**
     $$
     x = \frac{6 + 6}{10} = \frac{12}{10} = \frac{6}{5}
     $$
   
   - **Second Solution:**
     $$
     x = \frac{6 - 6}{10} = \frac{0}{10} = 0
     $$
   
   Both solutions are real numbers.

**Final Answer:**

**A.** The solution set is $$ \left\{ 0,\, \dfrac{6}{5} \right\} $$
The solution set is $$ \left\{ 0,\, \dfrac{6}{5} \right\} $$.

Real Tutor Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions