What are the solutions to the equation 12x^2-224x+768=0 ?

The solutions to the equation 12x^2-224x+768=0 are x=(4(7+sqrt(13)))/3 ,x=(4(7-sqrt(13)))/3

Find the zeros of 12x^2-224x+768=0

The zeros of 12x^2-224x+768=0 are x=(4(7+sqrt(13)))/3 ,x=(4(7-sqrt(13)))/3

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12 x^{2} - 224 x + 768 = 0

x = \frac{4 ( 7 + 13 )}{3}, x = \frac{4 ( 7 - 13 )}{3}

Decimal Notation

x = 14.14073 \dots, x = 4.52593 \dots

Solution steps

12 x^{2} - 224 x + 768 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 224 ) \pm ( - 224 ) ^{2} - 4 \cdot 12 \cdot 768}{2 \cdot 12}

(- 224)^{2} - 4 \cdot 12 \cdot 768 = 3213

x_{1, 2} = \frac{- ( - 224 ) \pm 32 13}{2 \cdot 12}

Separate the solutions

x_{1} = \frac{- ( - 224 ) + 32 13}{2 \cdot 12}, x_{2} = \frac{- ( - 224 ) - 32 13}{2 \cdot 12}

x = \frac{- ( - 224 ) + 32 13}{2 \cdot 12} : \frac{4 ( 7 + 13 )}{3}

x = \frac{- ( - 224 ) - 32 13}{2 \cdot 12} : \frac{4 ( 7 - 13 )}{3}

The solutions to the quadratic equation are:

x = \frac{4 ( 7 + 13 )}{3}, x = \frac{4 ( 7 - 13 )}{3}

3 x^{2} + 28 x + 9 = 0

(2 x - 3) (3 x - 2) = 0

x, z = 1 + x^{2} + y^{2}

5 x^{2} + 2 = 4 x

x^{2} + \frac{2}{5} x + 3

What are the solutions to the equation 12x^2-224x+768=0 ?
The solutions to the equation 12x^2-224x+768=0 are x=(4(7+sqrt(13)))/3 ,x=(4(7-sqrt(13)))/3
Find the zeros of 12x^2-224x+768=0
The zeros of 12x^2-224x+768=0 are x=(4(7+sqrt(13)))/3 ,x=(4(7-sqrt(13)))/3