Question

What is `x` if `2x-3/x=11`?

Answer 1

`x=(11+sqrt145)/4, (11-sqrt 145)/4`

Explanation:

`2x-3/x=11`

Multiply both sides by the LCD `x`.

`2x(x)-3/cancelx(cancel x)=11(x)=`

`2x^2-3=11x`

Move all terms to the left side.

`2x^2-3-11x=0`

Rearrange the terms.

`2x^2-11x-3`

Apply the quadratic formula.

`2x^2-11x-3` is in the form of a quadratic equation `ax+bx+c`, where `a=2, b=-11, and c=-3`.

Quadratic Formula

`x=(-b+-sqrt(b^2-4ac))/(2a)=`

`x=(-(-11)+-sqrt((-11^2)-(4*2*-3)))/(2*2)=`

`x=(11+-sqrt(121+24))/4=`

`x=(11+-sqrt(145))/4`

Solve for `x`.

`x=(11+sqrt145)/4, (11-sqrt 145)/4`