# How do you solve 2x^2 + 5x - 3 = 0?

Apr 10, 2017

See the entire solution process below:

#### Explanation:

We can factor the left side of the equation as:

$\left(2 x - 1\right) \left(x + 3\right) = 0$

We can now solve each term on the right side of the equation for $0$:

Solution 1)

$2 x - 1 = 0$

$2 x - 1 + \textcolor{red}{1} = 0 + \textcolor{red}{1}$

$2 x - 0 = 1$

$2 x = 1$

$\frac{2 x}{\textcolor{red}{2}} = \frac{1}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = \frac{1}{2}$

$x = \frac{1}{2}$

Solution 2)

$x + 3 = 0$

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

$x + 0 = - 3$

$x = - 3$

The solution is: $x = \frac{1}{2}$ and $x = - 3$