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

1 Answer

1 vote

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)

User Navid Rahmani
by
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