What are the solutions to the equation 12x^2-24x+5=0 ?

The solutions to the equation 12x^2-24x+5=0 are x=(6+sqrt(21))/6 ,x=(6-sqrt(21))/6

Find the zeros of 12x^2-24x+5=0

The zeros of 12x^2-24x+5=0 are x=(6+sqrt(21))/6 ,x=(6-sqrt(21))/6

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12 x^{2} - 24 x + 5 = 0

x = \frac{6 + 21}{6}, x = \frac{6 - 21}{6}

Decimal Notation

x = 1.76376 \dots, x = 0.23623 \dots

Solution steps

12 x^{2} - 24 x + 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 24 ) \pm ( - 24 ) ^{2} - 4 \cdot 12 \cdot 5}{2 \cdot 12}

(- 24)^{2} - 4 \cdot 12 \cdot 5 = 421

x_{1, 2} = \frac{- ( - 24 ) \pm 4 21}{2 \cdot 12}

Separate the solutions

x_{1} = \frac{- ( - 24 ) + 4 21}{2 \cdot 12}, x_{2} = \frac{- ( - 24 ) - 4 21}{2 \cdot 12}

x = \frac{- ( - 24 ) + 4 21}{2 \cdot 12} : \frac{6 + 21}{6}

x = \frac{- ( - 24 ) - 4 21}{2 \cdot 12} : \frac{6 - 21}{6}

The solutions to the quadratic equation are:

x = \frac{6 + 21}{6}, x = \frac{6 - 21}{6}

6 = 4 x - 5 x^{2}

a, an = 2 n^{2} - 1

20 - x = \frac{1}{324} x^{2} + 1

h^{2} = 49

\frac{1}{2} x^{2} - 3 x + 4 = 0

What are the solutions to the equation 12x^2-24x+5=0 ?
The solutions to the equation 12x^2-24x+5=0 are x=(6+sqrt(21))/6 ,x=(6-sqrt(21))/6
Find the zeros of 12x^2-24x+5=0
The zeros of 12x^2-24x+5=0 are x=(6+sqrt(21))/6 ,x=(6-sqrt(21))/6