Answer
$x\approx2.30$ and $x\approx-1.76$.
Work Step by Step
$2x^{2}-x+8=16$
Subtracting $16$ from both sides, we obtain
$2x^{2}-x+8-16=16-16$
$\implies 2x^{2}-x-8=0$
Comparing $2x^{2}-x-8=0$ with $ax^{2}+bx+c=0$, we see that $a=2, b=-1$ and $c=-8$.
Using the quadratic formula, we have
$x=\frac{-b\pm \sqrt {b^{2}-4ac}}{2a}=\frac{-(-1)\pm\sqrt {(-1)^{2}-4(2)(-8)}}{2(2)}$
$=\frac{1\pm\sqrt {65}}{4}$
So, the solutions are $x=\frac{1+\sqrt {65}}{4}\approx2.30$ and $x=\frac{1-\sqrt {65}}{4}\approx-1.76$.
