What are the solutions to the equation 12x^2-168x+432=0 ?

The solutions to the equation 12x^2-168x+432=0 are x=7+sqrt(13),x=7-sqrt(13)

Find the zeros of 12x^2-168x+432=0

The zeros of 12x^2-168x+432=0 are x=7+sqrt(13),x=7-sqrt(13)

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12 x^{2} - 168 x + 432 = 0

x = 7 + 13, x = 7 - 13

Decimal Notation

x = 10.60555 \dots, x = 3.39444 \dots

Solution steps

12 x^{2} - 168 x + 432 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 168 ) \pm ( - 168 ) ^{2} - 4 \cdot 12 \cdot 432}{2 \cdot 12}

(- 168)^{2} - 4 \cdot 12 \cdot 432 = 2413

x_{1, 2} = \frac{- ( - 168 ) \pm 24 13}{2 \cdot 12}

Separate the solutions

x_{1} = \frac{- ( - 168 ) + 24 13}{2 \cdot 12}, x_{2} = \frac{- ( - 168 ) - 24 13}{2 \cdot 12}

x = \frac{- ( - 168 ) + 24 13}{2 \cdot 12} : 7 + 13

x = \frac{- ( - 168 ) - 24 13}{2 \cdot 12} : 7 - 13

The solutions to the quadratic equation are:

x = 7 + 13, x = 7 - 13

x, z = y x^{2} z^{2} - x y^{4} + x y

y^{2} = (4430523)^{2} + (3166128)^{2}

15 x^{2} - 23 x - 10 = 0

x, 4 x^{2} + y^{2} + z^{2} = 1

p^{2} + \frac{p}{3} = \frac{2}{3} p

What are the solutions to the equation 12x^2-168x+432=0 ?
The solutions to the equation 12x^2-168x+432=0 are x=7+sqrt(13),x=7-sqrt(13)
Find the zeros of 12x^2-168x+432=0
The zeros of 12x^2-168x+432=0 are x=7+sqrt(13),x=7-sqrt(13)