# How do you use the quadratic formula to solve 3.8x^2=4.7x-2.1?

Sep 29, 2017

See a solution process below:

#### Explanation:

First, rewrite the equation as:

$3.8 {x}^{2} - \textcolor{red}{4.7 x} + \textcolor{b l u e}{2.1} = 4.7 x - \textcolor{red}{4.7 x} - 2.1 + \textcolor{b l u e}{2.1}$

$3.8 {x}^{2} - 4.7 x + 2.1 = 0 - 0$

$3.8 {x}^{2} - 4.7 x + 2.1 = 0$

Now, we can use the quadratic equation to solve this problem:

For $\textcolor{red}{a} {x}^{2} + \textcolor{b l u e}{b} x + \textcolor{g r e e n}{c} = 0$, the values of $x$ which are the solutions to the equation are given by:

$x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - \left(4 \textcolor{red}{a} \textcolor{g r e e n}{c}\right)}}{2 \cdot \textcolor{red}{a}}$

Substituting:

$\textcolor{red}{3.8}$ for $\textcolor{red}{a}$

$\textcolor{b l u e}{- 4.7}$ for $\textcolor{b l u e}{b}$

$\textcolor{g r e e n}{2.1}$ for $\textcolor{g r e e n}{c}$ gives:

$x = \frac{- \textcolor{b l u e}{\left(- 4.7\right)} \pm \sqrt{{\textcolor{b l u e}{\left(- 4.7\right)}}^{2} - \left(4 \cdot \textcolor{red}{3.8} \cdot \textcolor{g r e e n}{2.1}\right)}}{2 \cdot \textcolor{red}{3.8}}$

$x = \frac{4.7 \pm \sqrt{22.09 - 31.92}}{7.6}$

$x = \frac{4.7 \pm \sqrt{- 9.83}}{7.6}$