What are the solutions to the equation 78=138t-16t^2 ?

The solutions to the equation 78=138t-16t^2 are t=(69-sqrt(3513))/(16),t=(69+sqrt(3513))/(16)

Find the zeros of 78=138t-16t^2

The zeros of 78=138t-16t^2 are t=(69-sqrt(3513))/(16),t=(69+sqrt(3513))/(16)

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78 = 138 t - 16 t^{2}

t = \frac{69 - 3513}{16}, t = \frac{69 + 3513}{16}

Decimal Notation

t = 0.60808 \dots, t = 8.01691 \dots

Solution steps

78 = 138 t - 16 t^{2}

Switch sides

138 t - 16 t^{2} = 78

Move

78

to the left side

138 t - 16 t^{2} - 78 = 0

Write in the standard form

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

- 16 t^{2} + 138 t - 78 = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- 138 \pm 13 8 ^{2} - 4 ( - 16 ) ( - 78 )}{2 ( - 16 )}

13 8^{2} - 4 (- 16) (- 78) = 23513

t_{1, 2} = \frac{- 138 \pm 2 3513}{2 ( - 16 )}

Separate the solutions

t_{1} = \frac{- 138 + 2 3513}{2 ( - 16 )}, t_{2} = \frac{- 138 - 2 3513}{2 ( - 16 )}

t = \frac{- 138 + 2 3513}{2 ( - 16 )} : \frac{69 - 3513}{16}

t = \frac{- 138 - 2 3513}{2 ( - 16 )} : \frac{69 + 3513}{16}

The solutions to the quadratic equation are:

t = \frac{69 - 3513}{16}, t = \frac{69 + 3513}{16}

∣ 3 z + 5 ∣ > 2 z - 3

9 - 5

y + 3 = 0

3 x - 5 = 10

5 a^{2} + a

What are the solutions to the equation 78=138t-16t^2 ?
The solutions to the equation 78=138t-16t^2 are t=(69-sqrt(3513))/(16),t=(69+sqrt(3513))/(16)
Find the zeros of 78=138t-16t^2
The zeros of 78=138t-16t^2 are t=(69-sqrt(3513))/(16),t=(69+sqrt(3513))/(16)