Solve 3x^(3/2) - 9x^(1/2) -6x^(-1/2)

Question

Simplify the expression

\frac{3 x ^{2} x - 9 x \times x - 6 x}{x}

Show Solution

x = \frac{3 + 17}{2}

Alternative Form

x \approx 3.561553

Evaluate

3 x^{\frac{3}{2}} - 9 x^{\frac{1}{2}} - 6 x^{- \frac{1}{2}}

To find the roots of the expression,set the expression equal to 0

3 x^{\frac{3}{2}} - 9 x^{\frac{1}{2}} - 6 x^{- \frac{1}{2}} = 0

Find the domain

3 x^{\frac{3}{2}} - 9 x^{\frac{1}{2}} - 6 x^{- \frac{1}{2}} = 0, x > 0

Calculate

3 x^{\frac{3}{2}} - 9 x^{\frac{1}{2}} - 6 x^{- \frac{1}{2}} = 0

Rewrite the expression

More Steps

3 x^{\frac{3}{2}} - 9 x^{\frac{1}{2}} - \frac{6}{x ^{\frac{1}{2}}} = 0

Multiply both sides of the equation by LCD

(3 x^{\frac{3}{2}} - 9 x^{\frac{1}{2}} - \frac{6}{x ^{\frac{1}{2}}}) x^{\frac{1}{2}} = 0 \times x^{\frac{1}{2}}

Simplify the equation

More Steps

3 x^{2} - 9 x - 6 = 0 \times x^{\frac{1}{2}}

Any expression multiplied by 0 equals 0

3 x^{2} - 9 x - 6 = 0

Substitute a= 3,b= - 9 and c= - 6 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{9 \pm ( - 9 ) ^{2} - 4 \times 3 ( - 6 )}{2 \times 3}

Simplify the expression

x = \frac{9 \pm ( - 9 ) ^{2} - 4 \times 3 ( - 6 )}{6}

Simplify the expression

More Steps

x = \frac{9 \pm 153}{6}

Simplify the radical expression

More Steps

x = \frac{9 \pm 3 17}{6}

Separate the equation into 2 possible cases

x = \frac{9 + 3 17}{6} x = \frac{9 - 3 17}{6}

Simplify the expression

More Steps

x = \frac{3 + 17}{2} x = \frac{9 - 3 17}{6}

Simplify the expression

More Steps

x = \frac{3 + 17}{2} x = \frac{3 - 17}{2}

Check if the solution is in the defined range

x = \frac{3 + 17}{2} x = \frac{3 - 17}{2}, x > 0

Solution

x = \frac{3 + 17}{2}

Alternative Form

x \approx 3.561553

Show Solution