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

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

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

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

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

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

Decimal Notation

x = 10.90512 \dots, x = 3.09487 \dots

Solution steps

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

Write in the standard form

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

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}

0 = x^{2} - 6 x - 16

x^{2} - 6 x + 18

x^{2} - 6 x + 25

x^{2} + 6 x + c

x^{2} + 6 x - 5

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