Question

10. Solve: 3x² - x - 5 = 0

Answer 1

You have the following equation:

3x² - x - 5 = 0

In order to solve the previous equation, use the quadratic formula, given by:

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

where a, b anc c are the coeficients of the polynomial of the equation:

a = 3, b = -1, c = -5

replace the previous values into the quadratic formula:

$\begin{gathered} x=\frac{-(-1)\pm\sqrt[]{-(-1)^{2}-4(3)(-5)}}{2(3)} \\ x=\frac{1\pm\sqrt[]{-1+60}}{6} \\ x=\frac{1\pm\sqrt[]{59}}{6} \end{gathered}$

Then, you have the following two solutions:

x1 = (1 + √59)/6

x2 = (1 - √59)/6