We can use the quadratic formula:

[math]x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}[/math]

We will let [math]a = 1[/math], [math]b = 3[/math], [math]c = -4[/math]

Substituting the values into the equation:

[math]x = \frac{-3 \pm \sqrt{3^2 – 4(1)(-4)}}{2(1)}[/math]

Simplify:

[math]x = \frac{-3 \pm \sqrt{9 + 16}}{2}[/math]

[math]x = \frac{-3 \pm \sqrt{25}}{2}[/math]

Split the fraction:

[math]x = \frac{-3 + 5}{2}[/math], and [math]x = \frac{-3 – 5}{2}[/math]

Solutions:

[math]x = 1[/math] and [math]x = -4[/math]