What are the solutions to the equation 5/6 x^2-2/3 x= 1/3 ?

The solutions to the equation 5/6 x^2-2/3 x= 1/3 are x=(2+sqrt(14))/5 ,x=(2-sqrt(14))/5

Find the zeros of 5/6 x^2-2/3 x= 1/3

The zeros of 5/6 x^2-2/3 x= 1/3 are x=(2+sqrt(14))/5 ,x=(2-sqrt(14))/5

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\frac{5}{6} x^{2} - \frac{2}{3} x = \frac{1}{3}

x = \frac{2 + 14}{5}, x = \frac{2 - 14}{5}

Decimal Notation

x = 1.14833 \dots, x = - 0.34833 \dots

Solution steps

\frac{5}{6} x^{2} - \frac{2}{3} x = \frac{1}{3}

Find Least Common Multiplier of

6, 3 : 6

Multiply by LCM=

6

\frac{5}{6} x^{2} \cdot 6 - \frac{2}{3} x \cdot 6 = \frac{1}{3} \cdot 6

Simplify

5 x^{2} - 4 x = 2

Move

2

to the left side

5 x^{2} - 4 x - 2 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 5 ( - 2 )}{2 \cdot 5}

(- 4)^{2} - 4 \cdot 5 (- 2) = 214

x_{1, 2} = \frac{- ( - 4 ) \pm 2 14}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 14}{2 \cdot 5}, x_{2} = \frac{- ( - 4 ) - 2 14}{2 \cdot 5}

x = \frac{- ( - 4 ) + 2 14}{2 \cdot 5} : \frac{2 + 14}{5}

x = \frac{- ( - 4 ) - 2 14}{2 \cdot 5} : \frac{2 - 14}{5}

The solutions to the quadratic equation are:

x = \frac{2 + 14}{5}, x = \frac{2 - 14}{5}

y, x^{3} + x^{2} y + y^{2} = 0

5 x^{2} = 36 x + 32

x^{2} - 12 x + 36 = 3 x

x^{2} + 2 x - 50 = 0

5 x^{2} + 27 x + 10 = 0

What are the solutions to the equation 5/6 x^2-2/3 x= 1/3 ?
The solutions to the equation 5/6 x^2-2/3 x= 1/3 are x=(2+sqrt(14))/5 ,x=(2-sqrt(14))/5
Find the zeros of 5/6 x^2-2/3 x= 1/3
The zeros of 5/6 x^2-2/3 x= 1/3 are x=(2+sqrt(14))/5 ,x=(2-sqrt(14))/5