Answer
The first step is wrong and the correct answers are $x=\frac{1}{2}$ and $x=4$.
Work Step by Step
The given equation is
$\Rightarrow -2x^2+9x=4$
Subtract $4$ from each side.
$\Rightarrow -2x^2+9x-4=4-4$
Simplify.
$\Rightarrow -2x^2+9x-4=0$
Use Quadratic Formula.
$\Rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute $-2$ for $a,9$ for $b$ and $-4$ for $c$.
$\Rightarrow x=\frac{-9\pm\sqrt{(9)^2-4(-2)(-4)}}{2(-2)}$
Simplify.
$\Rightarrow x=\frac{-9\pm\sqrt{81-32}}{-4}$
$\Rightarrow x=\frac{-9\pm\sqrt{49}}{-4}$
$\Rightarrow x=\frac{-9\pm 7}{-4}$
The solutions are $x=\frac{-9+7}{-4}=\frac{-2}{-4}=\frac{1}{2}$ and $x=\frac{-9-7}{-4}=\frac{-16}{-4}=4$
Hence, the first step is wrong and the correct answers are $x=\frac{1}{2}$ and $x=4$.
