What are the solutions to the equation x^2= 5/6 x-1/8 ?

The solutions to the equation x^2= 5/6 x-1/8 are x=(5+sqrt(7))/(12),x=(5-sqrt(7))/(12)

Find the zeros of x^2= 5/6 x-1/8

The zeros of x^2= 5/6 x-1/8 are x=(5+sqrt(7))/(12),x=(5-sqrt(7))/(12)

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x^{2} = \frac{5}{6} x - \frac{1}{8}

x = \frac{5 + 7}{12}, x = \frac{5 - 7}{12}

Decimal Notation

x = 0.63714 \dots, x = 0.19618 \dots

Solution steps

x^{2} = \frac{5}{6} x - \frac{1}{8}

Find Least Common Multiplier of

6, 8 : 24

Multiply by LCM=

24

x^{2} \cdot 24 = \frac{5}{6} x \cdot 24 - \frac{1}{8} \cdot 24

Simplify

24 x^{2} = 20 x - 3

Move

3

to the left side

24 x^{2} + 3 = 20 x

Move

20 x

to the left side

24 x^{2} + 3 - 20 x = 0

Write in the standard form

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

24 x^{2} - 20 x + 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 20 ) \pm ( - 20 ) ^{2} - 4 \cdot 24 \cdot 3}{2 \cdot 24}

(- 20)^{2} - 4 \cdot 24 \cdot 3 = 47

x_{1, 2} = \frac{- ( - 20 ) \pm 4 7}{2 \cdot 24}

Separate the solutions

x_{1} = \frac{- ( - 20 ) + 4 7}{2 \cdot 24}, x_{2} = \frac{- ( - 20 ) - 4 7}{2 \cdot 24}

x = \frac{- ( - 20 ) + 4 7}{2 \cdot 24} : \frac{5 + 7}{12}

x = \frac{- ( - 20 ) - 4 7}{2 \cdot 24} : \frac{5 - 7}{12}

The solutions to the quadratic equation are:

x = \frac{5 + 7}{12}, x = \frac{5 - 7}{12}

12 x = 19

∣ 2 x - 1 ∣ = 7

2 x = - 10

5 x^{5} - 5 x (25 x^{2} - 144)

2 t^{2} + 3 t - 2

What are the solutions to the equation x^2= 5/6 x-1/8 ?
The solutions to the equation x^2= 5/6 x-1/8 are x=(5+sqrt(7))/(12),x=(5-sqrt(7))/(12)
Find the zeros of x^2= 5/6 x-1/8
The zeros of x^2= 5/6 x-1/8 are x=(5+sqrt(7))/(12),x=(5-sqrt(7))/(12)