Mathematico | Mathematico

The solutions of the equation

3 (x + 1) (x - 5) = (x + 3) (x + 5)

in simplest form are

a \pm b \sqrt{c}

Find the value of $a b c$ .

Hint

Expand both sides, collect everything on the left-hand-side.

Solution

We expand and simplify both sides

\begin{aligned} 3 (x + 1) (x - 5) & = (x + 3) (x + 5) \\ 3 x^{2} - 12 * x - 15 & = x^{2} + 8 x + 15 \\ 2 x^{2} - 20 x - 30 & = 0 \\ x & = \frac{20 \pm \sqrt{400 - 4 (2) (- 30)}}{2 (2)} \\ = 5 \pm 2 \sqrt{10} \end{aligned}