Question

Solve for x
(1/x) -2/3 = (4x)

Answer 1

The value of x is
`x=(-1+√(37))/(12)` and
`x=(-1-√(37))/(12)`

Explanation:

The equation is
`(1)/(x)-(2)/(3)=4 x`

Subtracting by
`4x` on both sides,

`(1)/(x)-(2)/(3)-4 x=0`

Taking LCM,

`(3-12 x^(2)-2 x)/(3 x)=0`

Multiplying by 3x on both sides,

`-12 x^(2)-2 x+3=0`

Dividing by (-) on both sides,

`12 x^(2)+2 x-3=0`

Using quadratic formula, we can solve for x.

`\begin{aligned}x &=\frac{-2 \pm \sqrt{2^(2)-4 \cdot 12 \cdot(-3)}}{2 \cdot 12} \\&=(-2 \pm √(4+144))/(2 \cdot 144) \\&=(-2 \pm √(148))/(24) \\&=(-2 \pm 2 √(37))/(24)\end{aligned}`

Taking out common term 2, we get,

`\begin{array}{l}{x=(-2(1 \pm √(37)))/(24)} \\{x=(-1 \pm √(37))/(12)}\end{array}`

Thus, the value of x is
`x=(-1+√(37))/(12)` and
`x=(-1-√(37))/(12)`