Question

Solve the equation by the method of your choice.
2 x squared minus 3 x equals 20
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Part 1
The solution set is StartSet nothing EndSet
  
.
​(Type an exact​ answer, using radicals as needed. Use a comma to separate answers as​ needed.)

Answer 1

To solve the equation \( 2x^2 - 3x = 20 \), we first move all terms to one side of the equation:

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

Now, we can solve this quadratic equation using the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In our equation, \( a = 2 \), \( b = -3 \), and \( c = -20 \).

First, we calculate the discriminant:

\[
b^2 - 4ac = (-3)^2 - 4 \cdot 2 \cdot (-20) = 9 + 160 = 169
\]

Now, we substitute back into the quadratic formula:

\[
x = \frac{-(-3) \pm \sqrt{169}}{2 \cdot 2}
\]

Simplifying this gives:

\[
x = \frac{3 \pm 13}{4}
\]

Now we calculate the two possible solutions:

1. \( x = \frac{3 + 13}{4} = \frac{16}{4} = 4 \)

2. \( x = \frac{3 - 13}{4} = \frac{-10}{4} = -\frac{5}{2} \)

Thus, the solution set is:

\[
\{ 4, -\frac{5}{2} \}
\]

So, the final answer is:

\[
\{ 4, -\frac{5}{2} \}
\]