# How do you solve 6x^2+5x+1=0?

Jul 12, 2015

The solutions are:
color(blue)(x=-1/2,x=-1/3

#### Explanation:

$6 {x}^{2} + 5 x + 1 = 0$
We can first factorise the expression and then find the solutions.

Factorising by splitting the middle term

$6 {x}^{2} + \textcolor{b l u e}{5 x} + 1 = 0$

$6 {x}^{2} \textcolor{b l u e}{+ 2 x + 3 x} + 1 = 0$

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

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

Now we equate the factors with zero to obtain the solutions:

2x+1 =0, color(blue)(x=-1/2

3x+1=0, color(blue)(x=-1/3