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

The solutions to the equation x(2x+1/3)-5x^2=3x-2 are x=-(4+sqrt(70))/9 ,x=(sqrt(70)-4)/9

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

The zeros of x(2x+1/3)-5x^2=3x-2 are x=-(4+sqrt(70))/9 ,x=(sqrt(70)-4)/9

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

x = - \frac{4 + 70}{9}, x = \frac{70 - 4}{9}

Decimal Notation

x = - 1.37406 \dots, x = 0.48517 \dots

Solution steps

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

Expand

x (2 x + \frac{1}{3}) - 5 x^{2} : - 3 x^{2} + \frac{1}{3} x

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

Move

2

to the left side

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

Move

3 x

to the left side

- 3 x^{2} - \frac{8}{3} x + 2 = 0

Write in the standard form

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

- 3 x^{2} - \frac{8 x}{3} + 2 = 0

Solve with the quadratic formula

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

(- \frac{8}{3})^{2} - 4 (- 3) \cdot 2 = \frac{2 70}{3}

x_{1, 2} = \frac{- ( - \frac{8}{3} ) \pm \frac{2 70}{3}}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- ( - \frac{8}{3} ) + \frac{2 70}{3}}{2 ( - 3 )}, x_{2} = \frac{- ( - \frac{8}{3} ) - \frac{2 70}{3}}{2 ( - 3 )}

x = \frac{- ( - \frac{8}{3} ) + \frac{2 70}{3}}{2 ( - 3 )} : - \frac{4 + 70}{9}

x = \frac{- ( - \frac{8}{3} ) - \frac{2 70}{3}}{2 ( - 3 )} : \frac{70 - 4}{9}

The solutions to the quadratic equation are:

x = - \frac{4 + 70}{9}, x = \frac{70 - 4}{9}

4 (x^{2} - 1) = 21

15 (2 a - 2) = 5 (a^{2} - 1)

2 n^{2} - 14 n + 3 = 3

s^{2} + 3 s + 4

x, x^{2} - 3 m x + 2 m^{2} = 0

What are the solutions to the equation x(2x+1/3)-5x^2=3x-2 ?
The solutions to the equation x(2x+1/3)-5x^2=3x-2 are x=-(4+sqrt(70))/9 ,x=(sqrt(70)-4)/9
Find the zeros of x(2x+1/3)-5x^2=3x-2
The zeros of x(2x+1/3)-5x^2=3x-2 are x=-(4+sqrt(70))/9 ,x=(sqrt(70)-4)/9