select the correct answer.\nwhat are the solutions of this quadratic equation?\n$6x^{2}+6 = 12x + 18$\na. $x…

Answer:

C. $x = 2\pm\sqrt{6}$

Explanation:

Step1: Rearrange to standard form

$6x^{2}-12x - 12=0$, then divide by 6 to get $x^{2}-2x - 2 = 0$.

Step2: Identify coefficients

For $x^{2}-2x - 2 = 0$, $a = 1$, $b=-2$, $c=-2$.

Step3: Use quadratic formula

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

Step4: Simplify expression

$x=\frac{2\pm\sqrt{4 + 8}}{2}=\frac{2\pm\sqrt{12}}{2}=\frac{2\pm2\sqrt{3}}{2}=2\pm\sqrt{6}$.