Start reordering the equation:
[tex]\begin{gathered} 113x^2+1=16x\text{ subtract 16x from both sides} \\ 113x^2+1-16x=16x-16x \\ 113x^2+1-16x=0\text{ reorder the terms} \\ 113x^2-16x+1=0 \end{gathered}[/tex]
Use the quadratic formula to find the roots:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\begin{cases}a=113 \\ b=-16 \\ c=1\end{cases} \\ x=\frac{-(-16)\pm\sqrt[]{(-16)^2-4(113)(1)}}{2(113)} \\ x=\frac{16\pm\sqrt[]{256-452}}{226} \\ x=\frac{16\pm\sqrt[]{-196}}{226}=\frac{16\pm\sqrt[]{196}\cdot\sqrt[]{-1}}{226} \\ x=\frac{16\pm14i}{226}\text{ simplify numbers} \\ x=\frac{8\pm7i}{113}\text{ the answers are} \\ x1=\frac{8}{113}+\frac{7i}{113}\text{ and }x2=\frac{8}{113}-\frac{7i}{113} \end{gathered}[/tex]
