Question 345958
(1)/(4)=3-2x-(1)/(x)+2 All / signs stand for +- and all  ~ signs stand for the square root.

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
3-2x-(1)/(x)+2=(1)/(4)

Add 2 to 3 to get 5.
5-2x-(1)/(x)=(1)/(4)

Find the LCD (least common denominator) of -2x+5-(1)/(x)+(1)/(4).
Least common denominator: 4x

Multiply each term in the equation by 4x in order to remove all the denominators from the equation.
-2x*4x+5*4x-(1)/(x)*4x=(1)/(4)*4x

Simplify the left-hand side of the equation by canceling the common factors.
-8x^(2)+20x-4=(1)/(4)*4x

Simplify the right-hand side of the equation by simplifying each term.
-8x^(2)+20x-4=x

Since x contains the variable to solve for, move it to the left-hand side of the equation by subtracting x from both sides.
-8x^(2)+20x-4-x=0

Since 20x and -x are like terms, add -x to 20x to get 19x.
-8x^(2)+19x-4=0

Multiply each term in the equation by -1.
-8x^(2)*-1+19x*-1-4*-1=0*-1

Simplify the left-hand side of the equation by multiplying out all the terms.
8x^(2)-19x+4=0*-1

Multiply 0 by -1 to get 0.
8x^(2)-19x+4=0

Use the quadratic formula to find the solutions.  In this case, the values are a=8, b=-19, and c=4.
x=(-b\~(b^(2)-4ac))/(2a) where ax^(2)+bx+c=0

Use the standard form of the equation to find a, b, and c for this quadratic.
a=8, b=-19, and c=4

Substitute in the values of a=8, b=-19, and c=4.
x=(-(-19)\~((-19)^(2)-4(8)(4)))/(2(8))

Multiply -1 by each term inside the parentheses.
x=(19\~((-19)^(2)-4(8)(4)))/(2(8))

Simplify the section inside the radical.
x=(19\~(233))/(2(8))

Simplify the denominator of the quadratic formula.
x=(19\~(233))/(16)

First, solve the + portion of \.
x=(19+~(233))/(16)

Next, solve the - portion of \.
x=(19-~(233))/(16)

The final answer is the combination of both solutions.
x=(19+~(233))/(16),(19-~(233))/(16)_x=2.14,0.23