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

The solutions to the equation 5/3 x^2-x= 1/3 are x=(3+sqrt(29))/(10),x=(3-sqrt(29))/(10)

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

The zeros of 5/3 x^2-x= 1/3 are x=(3+sqrt(29))/(10),x=(3-sqrt(29))/(10)

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

x = \frac{3 + 29}{10}, x = \frac{3 - 29}{10}

Decimal Notation

x = 0.83851 \dots, x = - 0.23851 \dots

Solution steps

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

Multiply both sides by

3

5 x^{2} - 3 x = 1

Move

1

to the left side

5 x^{2} - 3 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 5 ( - 1 )}{2 \cdot 5}

(- 3)^{2} - 4 \cdot 5 (- 1) = 29

x_{1, 2} = \frac{- ( - 3 ) \pm 29}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 29}{2 \cdot 5}, x_{2} = \frac{- ( - 3 ) - 29}{2 \cdot 5}

x = \frac{- ( - 3 ) + 29}{2 \cdot 5} : \frac{3 + 29}{10}

x = \frac{- ( - 3 ) - 29}{2 \cdot 5} : \frac{3 - 29}{10}

The solutions to the quadratic equation are:

x = \frac{3 + 29}{10}, x = \frac{3 - 29}{10}

x^{2} - 4 x - 25 = 0

- x^{2} - 13 x - 18 = - 3 x

\frac{41}{144} x^{2} + 1 = \frac{60}{7} x - \frac{444}{7}

x^{2} + 3 x - 1 = 0

s^{2} + 18 s + 81 = 0

What are the solutions to the equation 5/3 x^2-x= 1/3 ?
The solutions to the equation 5/3 x^2-x= 1/3 are x=(3+sqrt(29))/(10),x=(3-sqrt(29))/(10)
Find the zeros of 5/3 x^2-x= 1/3
The zeros of 5/3 x^2-x= 1/3 are x=(3+sqrt(29))/(10),x=(3-sqrt(29))/(10)