Question

What are the steps to solve6x^2+13x-5=0

Answer 1

`\begin{gathered} \text{Given} \\ 6x^2+13x-5=0 \end{gathered}`

The given quadratic equation is already in the standard form with the following coefficients.

a = 6, b = 13, and c = -5.

Using these coefficients, solve for x using the quadratic formula.

`\begin{gathered} x = ( -b \pm √(b^2 - 4ac))/( 2a ) \\ x = ( -13 \pm √(13^2 - 4(6)(-5)))/( 2(6) ) \\ x=(-13\pm√(169-(-120)))/(12) \\ x=(-13\pm√(169+120))/(12) \\ x = ( -13 \pm √(289))/( 12 ) \\ x = ( -13 \pm 17\, )/( 12 ) \end{gathered}`

Solve for the two values of x and we get

`\begin{gathered} x_1=(-13+17\,)/(12) \\ x_1=(4)/(12) \\ x_1=(1)/(3) \\ \\ x_2=(-13-17\,)/(12) \\ x_2=(-30)/(12) \\ x_2=-(5)/(2) \end{gathered}`

Therefore, the solution to the given equation is

`x=(1)/(3)\text{ and }x=-(5)/(2)`