Answer
$x\approx 2.19$ and $x\approx -1.94$.
Work Step by Step
The given equation is
$\Rightarrow 4x^2-x=17$
Subtract $17$ from each side.
$\Rightarrow 4x^2-x-17=17-17$
Simplify.
$\Rightarrow 4x^2-x-17=0$
The equation is not easily factorable, adn the numbers are somewhat large.
So, solve using the Quadratic Formula.
We have $a=4,b=-1$ and $c=-17$
Quadratic formula.
$\Rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute all the values into the formula.
$\Rightarrow x=\frac{-(-1)\pm\sqrt{(-1)^2-4(4)(-17)}}{2(4)}$
Clear the parentheses.
$\Rightarrow x=\frac{1\pm\sqrt{1+272}}{8}$
Simplify.
$\Rightarrow x=\frac{1\pm\sqrt{273}}{8}$
The solutions are.
$\Rightarrow x=\frac{1+\sqrt{273}}{8}$ and $x=\frac{1+\sqrt{273}}{8}$
Simplify.
$\Rightarrow x\approx 2.19$ and $x\approx -1.94$.
