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

1 Answer
Oct 28, 2015

Answer:

#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#