# How do you solve y = 3x^2 + 5x using the quadratic formula?

Jun 17, 2018

$x = 0 ,$$- \frac{5}{3}$

#### Explanation:

$y = 3 {x}^{2} + 5 x$ is a quadratic equation in standard form:

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

where:

$a = 3$, $b = 5$, $c = 0$

To solve the equation for $x$, substitute $0$ for $y$.

$0 = 3 {x}^{2} + 5 x$

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

Plug in the known values and solve.

$x = \frac{- 5 \pm \sqrt{{5}^{2} - 4 \cdot 3 \cdot 0}}{2 \cdot 3}$

$x = \frac{- 5 \pm \sqrt{25}}{6}$

$x = \frac{- 5 \pm 5}{6}$

$x = \frac{- 5 + 5}{6} ,$ $\frac{- 5 - 5}{6}$

$x = \frac{0}{6} , - \frac{10}{6}$

Simplify.

$x = 0 ,$$- \frac{5}{3}$