Answer
$x\approx -16.0577$ and $x\approx 17.0577$
Work Step by Step
Square the binomial to obtain
\begin{align*}
\ln{\left(4x^2-4x+1\right)}&=7\\\\
\end{align*}
Recall:
$$\ln{x}=n \longrightarrow e^n=x$$
Use the definition above to obtain:
\begin{align*}
e^7&=4x^2-4x+1\\\\
0&=4x^2-4x+1-e^7
\end{align*}
Recall:
The quadratic equation $ax^2+bx+c=0$ can be solved using the Quadratic Formula:
$$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$$
WIth $a=4, b=-4,$ and $c=1-e^7$, solve the equation using the Quadratic Formula to obtain:
\begin{align*}
x&=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(4)(1-e^7)}}{2(4)}\\\\
x&=\dfrac{4\pm\sqrt{16-16(1-e^7)}}{8}\\\\
x&=\dfrac{4\pm 132.4618078}{8}\\\\
x_1&=\dfrac{4-132.4618078}{8}\approx -16.0577\\\\
x_2&=\dfrac{4+132.4618078}{8}\approx 17.0577
\end{align*}
