What are the solutions to the equation 8-24x+12x^2=0 ?

The solutions to the equation 8-24x+12x^2=0 are x=(3+sqrt(3))/3 ,x=(3-sqrt(3))/3

Find the zeros of 8-24x+12x^2=0

The zeros of 8-24x+12x^2=0 are x=(3+sqrt(3))/3 ,x=(3-sqrt(3))/3

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8 - 24 x + 12 x^{2} = 0

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

Decimal Notation

x = 1.57735 \dots, x = 0.42264 \dots

Solution steps

8 - 24 x + 12 x^{2} = 0

Write in the standard form

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

12 x^{2} - 24 x + 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 24 ) \pm ( - 24 ) ^{2} - 4 \cdot 12 \cdot 8}{2 \cdot 12}

(- 24)^{2} - 4 \cdot 12 \cdot 8 = 83

x_{1, 2} = \frac{- ( - 24 ) \pm 8 3}{2 \cdot 12}

Separate the solutions

x_{1} = \frac{- ( - 24 ) + 8 3}{2 \cdot 12}, x_{2} = \frac{- ( - 24 ) - 8 3}{2 \cdot 12}

x = \frac{- ( - 24 ) + 8 3}{2 \cdot 12} : \frac{3 + 3}{3}

x = \frac{- ( - 24 ) - 8 3}{2 \cdot 12} : \frac{3 - 3}{3}

The solutions to the quadratic equation are:

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

u^{2} = - 10 u

x (x + 1) - 11 = x - 3

s^{2} + 8 s + 160 = 0

u^{2} = - 15 u

x^{2} + 31 = - 12 x

What are the solutions to the equation 8-24x+12x^2=0 ?
The solutions to the equation 8-24x+12x^2=0 are x=(3+sqrt(3))/3 ,x=(3-sqrt(3))/3
Find the zeros of 8-24x+12x^2=0
The zeros of 8-24x+12x^2=0 are x=(3+sqrt(3))/3 ,x=(3-sqrt(3))/3