Question

`8x ^(2) + 6x = 5`solve the quadratic equation using the quadratic formula

Answer 1

According to quadratic formula the soluion of th equadaratic equation

`ax^2+bx+c=0`

is given by:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Given data:

We are given th efollowing quadratic equation

`\begin{gathered} 8x^2+6x=5 \\ 8x^2+6x-5=0 \end{gathered}`

Now we have a=8, b=6 and c=-5.

So,

`\begin{gathered} \sqrt[]{b^2-4ac}=\sqrt[]{6^2-4(8)(-5)} \\ =\sqrt[]{36+260} \\ =\sqrt[]{196} \\ =14 \end{gathered}`

So, the solution of the quadaratic equation will be

`x=(-6\pm14)/(2(8))=(-6\pm14)/(16)`

So,

`x=(-6+14)/(16)=(8)/(16)=(1)/(2)`

and

`x=(-6-14)/(16)=(-20)/(16)=-(5)/(4)`

So, the solutions are

`x=-(5)/(4),x=(1)/(2)`

So, the correct option is C).