# How do you solve 4x^2 - 5x=0 using the quadratic formula?

Apr 11, 2018

$x = 0 \mathmr{and} x = \frac{5}{4}$

#### Explanation:

The quadratic formula for $a {x}^{2} + b x + c = 0$ is given by $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$a = 4 , b = - 5 , c = 0$

$\therefore x = \frac{- \left(- 5\right) \pm \sqrt{{\left(- 5\right)}^{2} - 4 \left(4\right) \left(0\right)}}{2 \left(4\right)}$

$x = \frac{5 \pm \sqrt{25}}{8}$

$x = \frac{5 \pm 5}{8} \implies x = 0 \mathmr{and} x = \frac{10}{8} = \frac{5}{4}$

Apr 11, 2018

$x = \frac{5}{4} \mathmr{and} x = 0$

#### Explanation:

The equation $y = 4 {x}^{2} - 5 x = 0$ is written in the form $y = a {x}^{2} + b x + c$,
so
$a = 4$, $b = - 5$, $c = 0$

The quadratic formula is $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Substitute the values of a, b and c into the formula

$x = \frac{5 \pm \sqrt{25}}{8}$

$x = \frac{5 + \sqrt{25}}{8}$ or $x = \frac{5 - \sqrt{25}}{8}$

$x = \frac{10}{8}$ or $x = \frac{0}{8}$

$x = \frac{5}{4} \mathmr{and} x = 0$

Apr 11, 2018

$x = 0 , \frac{5}{4}$

#### Explanation:

$4 {x}^{2} - 5 x = 0$ is a quadratic equation in standard form:

$a {x}^{2} + b x + c = 0$,

where:

$a = 4$, $b = - 5$, $c = 0$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Plug in the known values and solve.

$x = \frac{- \left(- 5\right) \pm \sqrt{{\left(- 5\right)}^{2} - 4 \cdot 4 \cdot 0}}{2 \cdot 4}$

Simplify.

$x = \frac{5 \pm \sqrt{25}}{8}$

$x = \frac{5 \pm 5}{8}$

$x = \frac{5 + 5}{8} = \frac{10}{8} = \frac{5}{4}$

$x = \frac{5 - 5}{8} = \frac{0}{8} = 0$

$x = 0 , \frac{5}{4}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$4 {x}^{2} - 5 x = 0$ can also be solved by factoring.

Factor out the common $x$.

$x \left(4 x - 5\right) = 0$

$x = 0$

$4 x - 5 = 0$

$4 x = 5$

$x = \frac{5}{4}$

$x = 0 , \frac{5}{4}$