What are the solutions to the equation (-16t^2+60t+180)=0 ?

The solutions to the equation (-16t^2+60t+180)=0 are t=-(3(sqrt(105)-5))/8 ,t=(3(5+sqrt(105)))/8

Find the zeros of (-16t^2+60t+180)=0

The zeros of (-16t^2+60t+180)=0 are t=-(3(sqrt(105)-5))/8 ,t=(3(5+sqrt(105)))/8

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(- 16 t^{2} + 60 t + 180) = 0

t = - \frac{3 ( 105 - 5 )}{8}, t = \frac{3 ( 5 + 105 )}{8}

Decimal Notation

t = - 1.96760 \dots, t = 5.71760 \dots

Solution steps

(- 16 t^{2} + 60 t + 180) = 0

Refine

- 16 t^{2} + 60 t + 180 = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- 60 \pm 6 0 ^{2} - 4 ( - 16 ) \cdot 180}{2 ( - 16 )}

6 0^{2} - 4 (- 16) \cdot 180 = 12105

t_{1, 2} = \frac{- 60 \pm 12 105}{2 ( - 16 )}

Separate the solutions

t_{1} = \frac{- 60 + 12 105}{2 ( - 16 )}, t_{2} = \frac{- 60 - 12 105}{2 ( - 16 )}

t = \frac{- 60 + 12 105}{2 ( - 16 )} : - \frac{3 ( 105 - 5 )}{8}

t = \frac{- 60 - 12 105}{2 ( - 16 )} : \frac{3 ( 5 + 105 )}{8}

The solutions to the quadratic equation are:

t = - \frac{3 ( 105 - 5 )}{8}, t = \frac{3 ( 5 + 105 )}{8}

x^{2} - \frac{4}{3} x = 0

2 x^{2} - 1 x - 3 = 0

7 x^{2} = - 21 x

2 x^{2} + 8 = 40

120 = 20 x + 5 x^{2}

What are the solutions to the equation (-16t^2+60t+180)=0 ?
The solutions to the equation (-16t^2+60t+180)=0 are t=-(3(sqrt(105)-5))/8 ,t=(3(5+sqrt(105)))/8
Find the zeros of (-16t^2+60t+180)=0
The zeros of (-16t^2+60t+180)=0 are t=-(3(sqrt(105)-5))/8 ,t=(3(5+sqrt(105)))/8