which equation shows the quadratic formula used correctly to solve 7x² = 9 + x for x?\nx=\frac{-1pmsqrt{(1)^{…

Explanation:

Step1: Rewrite the equation in standard form

First, rewrite $7x^{2}=9 + x$ as $7x^{2}-x - 9=0$. For a quadratic equation $ax^{2}+bx + c = 0$, here $a = 7$, $b=-1$, and $c=-9$.

Step2: Recall the quadratic formula

The quadratic formula for solving $ax^{2}+bx + c = 0$ for $x$ is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Substitute values of a, b, c

Substitute $a = 7$, $b=-1$, and $c=-9$ into the quadratic formula. We get $x=\frac{-(-1)\pm\sqrt{(-1)^{2}-4(7)(-9)}}{2(7)}=\frac{1\pm\sqrt{(-1)^{2}+4(7)(9)}}{2(7)}$.

Answer:

$x=\frac{1\pm\sqrt{(-1)^{2}+4(7)(9)}}{2(7)}$ (the last option)