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

The solutions to the equation (x^2-1)/2 =(4x)/3 are x=3,x=-1/3

Find the zeros of (x^2-1)/2 =(4x)/3

The zeros of (x^2-1)/2 =(4x)/3 are x=3,x=-1/3

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\frac{x ^{2} - 1}{2} = \frac{4 x}{3}

x = 3, x = - \frac{1}{3}

Decimal

x = 3, x = - 0.33333 \dots

Solution steps

\frac{x ^{2} - 1}{2} = \frac{4 x}{3}

Find Least Common Multiplier of

2, 3 : 6

Multiply by LCM=

6

\frac{x ^{2} - 1}{2} \cdot 6 = \frac{4 x}{3} \cdot 6

Simplify

3 (x^{2} - 1) = 8 x

Expand

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

3 x^{2} - 3 = 8 x

Move

8 x

to the left side

3 x^{2} - 3 - 8 x = 0

Write in the standard form

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

3 x^{2} - 8 x - 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 3 ( - 3 )}{2 \cdot 3}

(- 8)^{2} - 4 \cdot 3 (- 3) = 10

x_{1, 2} = \frac{- ( - 8 ) \pm 10}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 10}{2 \cdot 3}, x_{2} = \frac{- ( - 8 ) - 10}{2 \cdot 3}

x = \frac{- ( - 8 ) + 10}{2 \cdot 3} : 3

x = \frac{- ( - 8 ) - 10}{2 \cdot 3} : - \frac{1}{3}

The solutions to the quadratic equation are:

x = 3, x = - \frac{1}{3}

x, 4 x^{2} = 9 x - 2

x^{2} + 40 = 14 x

x^{2} - (a + 2) x = - 2 a

2 x^{2} = 400

(x + 2)^{2} + (x - 2)^{2} = 0

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