What are the solutions to the equation 1/3 (u-3/2)(u+3/2)=u(u/3 1/4) ?

The solutions to the equation 1/3 (u-3/2)(u+3/2)=u(u/3 1/4) are u=sqrt(3),u=-sqrt(3)

Find the zeros of 1/3 (u-3/2)(u+3/2)=u(u/3 1/4)

The zeros of 1/3 (u-3/2)(u+3/2)=u(u/3 1/4) are u=sqrt(3),u=-sqrt(3)

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\frac{1}{3} (u - \frac{3}{2}) (u + \frac{3}{2}) = u (\frac{u}{3} \frac{1}{4})

u = 3, u = - 3

Decimal Notation

u = 1.73205 \dots, u = - 1.73205 \dots

Solution steps

\frac{1}{3} (u - \frac{3}{2}) (u + \frac{3}{2}) = u (\frac{u}{3} \cdot \frac{1}{4})

Expand

\frac{1}{3} (u - \frac{3}{2}) (u + \frac{3}{2}) : \frac{1}{3} u^{2} - \frac{3}{4}

Expand

u (\frac{u}{3} \cdot \frac{1}{4}) : \frac{u ^{2}}{12}

\frac{1}{3} u^{2} - \frac{3}{4} = \frac{u ^{2}}{12}

Move

\frac{3}{4}

to the right side

\frac{1}{3} u^{2} = \frac{u ^{2}}{12} + \frac{3}{4}

Move

\frac{u ^{2}}{12}

to the left side

\frac{u ^{2}}{4} = \frac{3}{4}

Multiply both sides by

4

u^{2} = 3

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = 3, u = - 3

2 x^{2} - 10 x = 0

x - 3 - (- x (x + 1) + 4) - 5 = (- x + 6)

2 x^{2} - 378.4 x + 17856 = 0

2 x^{2} - x + 6

(2 x + 3)^{2} = 1

What are the solutions to the equation 1/3 (u-3/2)(u+3/2)=u(u/3 1/4) ?
The solutions to the equation 1/3 (u-3/2)(u+3/2)=u(u/3 1/4) are u=sqrt(3),u=-sqrt(3)
Find the zeros of 1/3 (u-3/2)(u+3/2)=u(u/3 1/4)
The zeros of 1/3 (u-3/2)(u+3/2)=u(u/3 1/4) are u=sqrt(3),u=-sqrt(3)