Question

Solve for x. Write both solutions, separated by acomma.6x² + 7x+2=0

Answer 1

Explanation

We are given the following:

`6x^2+7x+2=0`

We are required to solve the equation above.

Using the quadratic formula, we have:

`\begin{gathered} If\text{ }ax^2+bx+c=0,\text{ }then \\ x=(-b\pm√(b^2-4ac))/(2a) \end{gathered}`
`\begin{gathered} 6x^2+7x+2=0 \\ where \\ a=6,b=7,c=2 \\ x=(-7\pm√(7^2-4(6)(2)))/(2(6)) \\ x=(-7\pm√(49-48))/(12) \\ x=(-7\pm√(1))/(12)=(-7\pm1)/(12) \\ x_1=(-7+1)/(12),x_2=(-7-1)/(12) \\ x_1=(-6)/(12),x_2=(-8)/(12) \\ x_1=(-1)/(2),x_2=(-2)/(3) \end{gathered}`

Hence, the answer is:

`x_(1)=(-1)/(2), x_(2)=(-2)/(3)`