# Which equation shows the quadratic formula used correctly to solve 7x^{2} = 9 + x for x?

**Solution:**

Given that:

7x^{2} = 9 + x

The first step is to arrange all the terms to the left-hand side and equate it to 0.

7x^{2} - x - 9 = 0

The standard formula to evaluate the quadratic equation ax^{2} + bx + c = 0 is

\( x = \frac{-b\pm \sqrt{b^{2}-4ac}}{2a} \)

By comparing the given equation to the standard form

a = 7

b = - 1

c = - 9

\( \\x = \frac{-(-1)\pm \sqrt{(-1)^{2}-4\times 7\times -9}}{2\times 7} \\ \\x=\frac{1\pm \sqrt{253}}{14} \)

Therefore, the quadratic formula used correctly to solve 7x^{2} = 9 + x for x is \( x=\frac{1\pm \sqrt{253}}{14} \).

## Which equation shows the quadratic formula used correctly to solve 7x^{2} = 9 + x for x?

**Summary: **

The equation which shows the quadratic formula used correctly to solve 7x^{2} = 9 + x for x is \( x=\frac{1\pm \sqrt{253}}{14} \)