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

The solutions to the equation (u^2-1)/2 = u/3 are u=(1+sqrt(10))/3 ,u=(1-sqrt(10))/3

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

The zeros of (u^2-1)/2 = u/3 are u=(1+sqrt(10))/3 ,u=(1-sqrt(10))/3

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

u = \frac{1 + 10}{3}, u = \frac{1 - 10}{3}

Decimal

u = 1.38742 \dots, u = - 0.72075 \dots

Solution steps

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

Find Least Common Multiplier of

2, 3 : 6

Multiply by LCM=

6

\frac{u ^{2} - 1}{2} \cdot 6 = \frac{u}{3} \cdot 6

Simplify

3 (u^{2} - 1) = 2 u

Expand

3 (u^{2} - 1) : 3 u^{2} - 3

3 u^{2} - 3 = 2 u

Move

2 u

to the left side

3 u^{2} - 3 - 2 u = 0

Write in the standard form

a x^{2} + b x + c = 0

3 u^{2} - 2 u - 3 = 0

Solve with the quadratic formula

u_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 3 ( - 3 )}{2 \cdot 3}

(- 2)^{2} - 4 \cdot 3 (- 3) = 210

u_{1, 2} = \frac{- ( - 2 ) \pm 2 10}{2 \cdot 3}

Separate the solutions

u_{1} = \frac{- ( - 2 ) + 2 10}{2 \cdot 3}, u_{2} = \frac{- ( - 2 ) - 2 10}{2 \cdot 3}

u = \frac{- ( - 2 ) + 2 10}{2 \cdot 3} : \frac{1 + 10}{3}

u = \frac{- ( - 2 ) - 2 10}{2 \cdot 3} : \frac{1 - 10}{3}

The solutions to the quadratic equation are:

u = \frac{1 + 10}{3}, u = \frac{1 - 10}{3}

2 x^{2} - 8 x + 5 = 0

- 12 + 12 x - 3 x^{2} = 0

x^{2} + 5 x - \frac{7}{4} = 0

x^{2} - 11 x + 22 = - 2

4 x^{2} + 56 x + 144 = 0

What are the solutions to the equation (u^2-1)/2 = u/3 ?
The solutions to the equation (u^2-1)/2 = u/3 are u=(1+sqrt(10))/3 ,u=(1-sqrt(10))/3
Find the zeros of (u^2-1)/2 = u/3
The zeros of (u^2-1)/2 = u/3 are u=(1+sqrt(10))/3 ,u=(1-sqrt(10))/3