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

Feb 19, 2017

See the entire solution process below:

#### Explanation:

First, add $\textcolor{red}{3 {x}^{2}}$ to each side of the equation:

$\textcolor{red}{3 {x}^{2}} - 5 x = \textcolor{red}{3 {x}^{2}} - 3 {x}^{2}$

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

Now, factor an $x$ out of the expression on the left side of the equation:

$x \left(3 x - 5\right) = 0$

Now, we can find the two solutions by equating each of the terms to $0$ and solving:

Solution 1)

$x = 0$

Solution 2)

$3 x - 5 = 0$

$3 x - 5 + \textcolor{red}{5} = 0 + \textcolor{red}{5}$

$3 x - 0 = 5$

$3 x = 5$

$\frac{3 x}{\textcolor{red}{3}} = \frac{5}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} = \frac{5}{3}$

$x = \frac{5}{3}$

The solution is: $x = 0$ and $x = \frac{5}{3}$