# How do you solve 2.3x^2-1.4x=6.8 using the quadratic formula?

Aug 21, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{6.8}$ from each side of the equation to put the equation in standard form:

$2.3 {x}^{2} - 1.4 x - \textcolor{red}{6.8} = 6.8 - \textcolor{red}{6.8}$

$2.3 {x}^{2} - 1.4 x - 6.8 = 0$

We can now 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:

$\textcolor{red}{2.3}$ for $\textcolor{red}{a}$

$\textcolor{b l u e}{- 1.4}$ for $\textcolor{b l u e}{b}$

$\textcolor{g r e e n}{- 6.8}$ for $\textcolor{g r e e n}{c}$ gives:

$x = \frac{- \textcolor{b l u e}{\left(- 1.4\right)} \pm \sqrt{{\textcolor{b l u e}{\left(- 1.4\right)}}^{2} - \left(4 \cdot \textcolor{red}{2.3} \cdot \textcolor{g r e e n}{- 6.8}\right)}}{2 \cdot \textcolor{red}{2.3}}$

$x = \frac{\textcolor{b l u e}{1.4} \pm \sqrt{\textcolor{b l u e}{1.96} - \left(- 62.56\right)}}{4.6}$

$x = \frac{\textcolor{b l u e}{1.4} \pm \sqrt{\textcolor{b l u e}{1.96} + 62.56}}{4.6}$

$x = \frac{\textcolor{b l u e}{1.4} \pm \sqrt{64.52}}{4.6}$

$x = \frac{\textcolor{b l u e}{1.4} \pm \sqrt{4 \cdot 16.13}}{4.6}$

$x = \frac{\textcolor{b l u e}{1.4} \pm \sqrt{4} \sqrt{16.13}}{4.6}$

$x = \frac{\textcolor{b l u e}{1.4} \pm 2 \sqrt{16.13}}{4.6}$

$x = \frac{\textcolor{b l u e}{1.4} - 2 \sqrt{16.13}}{4.6}$ and $x = \frac{\textcolor{b l u e}{1.4} + 2 \sqrt{16.13}}{4.6}$

$x = \frac{\textcolor{b l u e}{\left(2 \cdot 0.7\right)} - 2 \sqrt{16.13}}{2 \cdot 2.3}$ and $x = \frac{\textcolor{b l u e}{\left(2 \cdot 0.7\right)} + 2 \sqrt{16.13}}{2 \cdot 2.3}$

$x = \frac{\textcolor{b l u e}{0.7} - \sqrt{16.13}}{2.3}$ and $x = \frac{\textcolor{b l u e}{0.7} + \sqrt{16.13}}{2.3}$