which are the solutions of the quadratic equation?\n$x^{2}=9x + 6$\n$\frac{-9-sqrt{105}}{2},\frac{-9+sqrt{105…

Explanation:

Step1: Rearrange to standard form

$x^{2}-9x - 6=0$. For a quadratic equation $ax^{2}+bx + c = 0$, here $a = 1$, $b=-9$, $c=-6$.

Step2: Apply quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 1$, $b=-9$, $c=-6$ into it. First calculate the discriminant $\Delta=b^{2}-4ac=(-9)^{2}-4\times1\times(-6)=81 + 24=105$.

Step3: Find the solutions

$x=\frac{-(-9)\pm\sqrt{105}}{2\times1}=\frac{9\pm\sqrt{105}}{2}$, so the solutions are $\frac{9 - \sqrt{105}}{2}$ and $\frac{9+\sqrt{105}}{2}$.

Answer:

C. $\frac{9 - \sqrt{105}}{2}$, $\frac{9+\sqrt{105}}{2}$