# Which of the graphs below correctly solves for x in the equation −x^{2} + 2x + 6 = 2x − 3?

Quadratic equations are those equations whose degree is equal to two. They are used for calculations in many fields of engineering and science as well as advanced mathematics.

## Answer: The solution of the equation given is x = 3 and x = -3. It is represented as two straight lines on the cartesian plane.

Let's understand the solution in detail.

**Explanation:**

Given equation: -x^{2} + 2x + 6 = 2x − 3

Now, to solve the equation for x, we follow the steps below:

⇒ −x^{2} + 2x + 6 = 2x − 3

⇒ −x^{2} + 2x − 2x = −6 − 3

⇒ −x^{2} = −9

⇒ x^{2} = 9

Hence, x = 3, or x = -3.

Now, we plot the result on the graph below.

Therefore, The graph cuts the x-axes at (-3, 0) and (3, 0).

### Hence, the solution of the equation given is x = 3 and x = -3. It is represented as two straight lines on the cartesian plane.

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