What are the solutions to the equation 12x^2-168x+405=0 ?

The solutions to the equation 12x^2-168x+405=0 are x=(14+sqrt(61))/2 ,x=(14-sqrt(61))/2

Find the zeros of 12x^2-168x+405=0

The zeros of 12x^2-168x+405=0 are x=(14+sqrt(61))/2 ,x=(14-sqrt(61))/2

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12 x^{2} - 168 x + 405 = 0

x = \frac{14 + 61}{2}, x = \frac{14 - 61}{2}

Decimal Notation

x = 10.90512 \dots, x = 3.09487 \dots

Solution steps

12 x^{2} - 168 x + 405 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 168 ) \pm ( - 168 ) ^{2} - 4 \cdot 12 \cdot 405}{2 \cdot 12}

(- 168)^{2} - 4 \cdot 12 \cdot 405 = 1261

x_{1, 2} = \frac{- ( - 168 ) \pm 12 61}{2 \cdot 12}

Separate the solutions

x_{1} = \frac{- ( - 168 ) + 12 61}{2 \cdot 12}, x_{2} = \frac{- ( - 168 ) - 12 61}{2 \cdot 12}

x = \frac{- ( - 168 ) + 12 61}{2 \cdot 12} : \frac{14 + 61}{2}

x = \frac{- ( - 168 ) - 12 61}{2 \cdot 12} : \frac{14 - 61}{2}

The solutions to the quadratic equation are:

x = \frac{14 + 61}{2}, x = \frac{14 - 61}{2}

8 (4 x + 6) = 7 (3 x + 7) - 23

\frac{- 12 + x}{11} = - 3

7 x^{2} - 63 = 0

20 x y - 16 x - 5 y + 4

0.5 p - 3.45 = 1.2

What are the solutions to the equation 12x^2-168x+405=0 ?
The solutions to the equation 12x^2-168x+405=0 are x=(14+sqrt(61))/2 ,x=(14-sqrt(61))/2
Find the zeros of 12x^2-168x+405=0
The zeros of 12x^2-168x+405=0 are x=(14+sqrt(61))/2 ,x=(14-sqrt(61))/2