Solve for the x- values
2
3x+4
・＝
x+6
2 + 6x
「Al x =0,6
「BIx =6,4
[CIr =4,-6
[Dr=-6,-4
We are given the equation:
$\frac{3x+4}{x+6} = \frac{2}{2+6x}$
First, cross-multiply to get:
$(3x+4)(2+6x) = (x+6)(2)$
Now, expand both sides:
$6x^2 + 12x + 6x + 8 = 2x + 12$
Simplify:
$6x^2 + 18x + 8 = 2x + 12$
Subtract $2x + 12$ from both sides:
$6x^2 + 16x - 4 = 0$
Now, divide by 2 to simplify:
$3x^2 + 8x - 2 = 0$
To solve the quadratic equation $3x^2 + 8x - 2 = 0$, use the quadratic formula:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
In this case, $a = 3$, $b = 8$, and $c = -2$. Plug these in to get:
$x = \frac{-8 \pm \sqrt{8^2 - 4(3)(-2)}}{2(3)}$
$x = \frac{-8 \pm \sqrt{64 + 24}}{6}$
$x = \frac{-8 \pm \sqrt{88}}{6}$
The two possible values of $x$ are:
$x = \frac{-8 + \sqrt{88}}{6}$ and $x = \frac{-8 - \sqrt{88}}{6}$
These don't simplify to any of the given answer choices, so it seems there may be an error in the answer choices themselves.