Answer
$\displaystyle \{0,\frac{5}{4}\}$
Work Step by Step
Write in standard form (subtract 5x from both sides)
$0=4x^{2}-5x$
$4x^{2}-5x=0$
The quicker way to solve this would be to factor the LHS,
but the exercise here is to use the quadratic formula.
STEP 1. Identify the coefficients
$a=4, b=-5, c=0$
STEP 2. Check the discriminant for the type and number of solutions.
$b^{2}-4ac=25-4(1)(0)=25\gt 0$
so there are two unequal real solutions.
STEP 3. Apply the quadratic formula
$x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$x=\displaystyle \frac{5\pm\sqrt{25}}{2(4)}$
$x=\displaystyle \frac{5\pm 5}{8}$
So, either $x=\displaystyle \frac{10}{8}=\frac{5}{4}$
or
$x=0$
Solution set = $\displaystyle \{0,\frac{5}{4}\}$
