What are the solutions to the equation 100+60x-12x^2=0 ?

The solutions to the equation 100+60x-12x^2=0 are x=-(5(sqrt(21)-3))/6 ,x=(5(3+sqrt(21)))/6

Find the zeros of 100+60x-12x^2=0

The zeros of 100+60x-12x^2=0 are x=-(5(sqrt(21)-3))/6 ,x=(5(3+sqrt(21)))/6

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100 + 60 x - 12 x^{2} = 0

x = - \frac{5 ( 21 - 3 )}{6}, x = \frac{5 ( 3 + 21 )}{6}

Decimal Notation

x = - 1.31881 \dots, x = 6.31881 \dots

Solution steps

100 + 60 x - 12 x^{2} = 0

Write in the standard form

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

- 12 x^{2} + 60 x + 100 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 60 \pm 6 0 ^{2} - 4 ( - 12 ) \cdot 100}{2 ( - 12 )}

6 0^{2} - 4 (- 12) \cdot 100 = 2021

x_{1, 2} = \frac{- 60 \pm 20 21}{2 ( - 12 )}

Separate the solutions

x_{1} = \frac{- 60 + 20 21}{2 ( - 12 )}, x_{2} = \frac{- 60 - 20 21}{2 ( - 12 )}

x = \frac{- 60 + 20 21}{2 ( - 12 )} : - \frac{5 ( 21 - 3 )}{6}

x = \frac{- 60 - 20 21}{2 ( - 12 )} : \frac{5 ( 3 + 21 )}{6}

The solutions to the quadratic equation are:

x = - \frac{5 ( 21 - 3 )}{6}, x = \frac{5 ( 3 + 21 )}{6}

\frac{a x ^{2}}{4} + \frac{x}{2} = \frac{2}{a}

x, 6 x^{2} = 7 x y + 20 y^{2}

5 x^{2} - x^{2} = 2 x^{2} + 72

x, x^{2} + y^{2} - 2 x + 2 y + 11 = 0

(b + 3)^{2} = 25

What are the solutions to the equation 100+60x-12x^2=0 ?
The solutions to the equation 100+60x-12x^2=0 are x=-(5(sqrt(21)-3))/6 ,x=(5(3+sqrt(21)))/6
Find the zeros of 100+60x-12x^2=0
The zeros of 100+60x-12x^2=0 are x=-(5(sqrt(21)-3))/6 ,x=(5(3+sqrt(21)))/6