Question

For x. Write both solutions6x²-x-15 = 0

Answer 1

Given:

`6x^2-x-15=0`

Required:

To find the solution.

Step-by-step explanation:

Consider

`6x^2-x-15=0`

Here

`\begin{gathered} a=6 \\ b=-1 \\ c=-15 \end{gathered}`
`x=(-b\pm√(b^2-4ac))/(2a)`

Here

`\begin{gathered} x=(-(-1)\pm√(1-4(6)(-15)))/(2(6)) \\ \\ =(1\pm√(1+360))/(12) \\ \\ =(1\pm√(361))/(12) \\ \\ =(1\pm19)/(12) \end{gathered}`

Now

`\begin{gathered} x=(1+19)/(12) \\ \\ =(20)/(12) \\ \\ =(5)/(3) \end{gathered}`

And

`\begin{gathered} x=(1-19)/(12) \\ \\ =-(18)/(12) \\ \\ =-(3)/(2) \\ \end{gathered}`

Final Answer:

`x=(5)/(3),-(3)/(2)`