which are the solutions of the quadratic equation?\n$x^{2}=9x + 6$\n$\\frac{-9-sqrt{105}}{2},\\frac{-9+sqrt{1…

which are the solutions of the quadratic equation?\n$x^{2}=9x + 6$\n$\\frac{-9-sqrt{105}}{2},\\frac{-9+sqrt{105}}{2}$\n$\\frac{-9-sqrt{57}}{2},\\frac{-9+sqrt{57}}{2}$\n$\\frac{9-sqrt{105}}{2},\\frac{9+sqrt{105}}{2}$\n$\\frac{9-sqrt{57}}{2},\\frac{9+sqrt{57}}{2}$

which are the solutions of the quadratic equation?\n$x^{2}=9x + 6$\n$\\frac{-9-sqrt{105}}{2},\\frac{-9+sqrt{105}}{2}$\n$\\frac{-9-sqrt{57}}{2},\\frac{-9+sqrt{57}}{2}$\n$\\frac{9-sqrt{105}}{2},\\frac{9+sqrt{105}}{2}$\n$\\frac{9-sqrt{57}}{2},\\frac{9+sqrt{57}}{2}$

Answer

Explanation:

Step1: Rewrite in standard form

$x^{2}-9x - 6=0$

Step2: Identify coefficients

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

Step3: Apply quadratic formula

$x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=\frac{-(-9)\pm\sqrt{(-9)^{2}-4\times1\times(-6)}}{2\times1}$

Step4: Simplify expression

$x=\frac{9\pm\sqrt{81 + 24}}{2}=\frac{9\pm\sqrt{105}}{2}$

Answer:

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