What are the solutions to the equation x^2-8/3 x-12=0 ?

The solutions to the equation x^2-8/3 x-12=0 are x=(2(2+sqrt(31)))/3 ,x=(2(2-sqrt(31)))/3

Find the zeros of x^2-8/3 x-12=0

The zeros of x^2-8/3 x-12=0 are x=(2(2+sqrt(31)))/3 ,x=(2(2-sqrt(31)))/3

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x^{2} - \frac{8}{3} x - 12 = 0

x = \frac{2 ( 2 + 31 )}{3}, x = \frac{2 ( 2 - 31 )}{3}

Decimal Notation

x = 5.04517 \dots, x = - 2.37850 \dots

Solution steps

x^{2} - \frac{8}{3} x - 12 = 0

Multiply both sides by

3

3 x^{2} - 8 x - 36 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 3 ( - 36 )}{2 \cdot 3}

(- 8)^{2} - 4 \cdot 3 (- 36) = 431

x_{1, 2} = \frac{- ( - 8 ) \pm 4 31}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 4 31}{2 \cdot 3}, x_{2} = \frac{- ( - 8 ) - 4 31}{2 \cdot 3}

x = \frac{- ( - 8 ) + 4 31}{2 \cdot 3} : \frac{2 ( 2 + 31 )}{3}

x = \frac{- ( - 8 ) - 4 31}{2 \cdot 3} : \frac{2 ( 2 - 31 )}{3}

The solutions to the quadratic equation are:

x = \frac{2 ( 2 + 31 )}{3}, x = \frac{2 ( 2 - 31 )}{3}

x^{2} + 16 x + c = 0

x^{2} - 6 x = - 6 x + 4

3 n^{2} - 10 n - 10 = 3 n

x^{2} = 9 (x + 4)

16 w^{2} + 25 = 40 w

What are the solutions to the equation x^2-8/3 x-12=0 ?
The solutions to the equation x^2-8/3 x-12=0 are x=(2(2+sqrt(31)))/3 ,x=(2(2-sqrt(31)))/3
Find the zeros of x^2-8/3 x-12=0
The zeros of x^2-8/3 x-12=0 are x=(2(2+sqrt(31)))/3 ,x=(2(2-sqrt(31)))/3