What are the solutions to the equation -3t(t+2)=-5 ?

The solutions to the equation -3t(t+2)=-5 are t=-(3+2sqrt(6))/3 ,t=(2sqrt(6)-3)/3

Find the zeros of -3t(t+2)=-5

The zeros of -3t(t+2)=-5 are t=-(3+2sqrt(6))/3 ,t=(2sqrt(6)-3)/3

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- 3 t (t + 2) = - 5

t = - \frac{3 + 2 6}{3}, t = \frac{2 6 - 3}{3}

Decimal Notation

t = - 2.63299 \dots, t = 0.63299 \dots

Solution steps

- 3 t (t + 2) = - 5

Expand

- 3 t (t + 2) : - 3 t^{2} - 6 t

- 3 t^{2} - 6 t = - 5

Move

5

to the left side

- 3 t^{2} - 6 t + 5 = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 ( - 3 ) \cdot 5}{2 ( - 3 )}

(- 6)^{2} - 4 (- 3) \cdot 5 = 46

t_{1, 2} = \frac{- ( - 6 ) \pm 4 6}{2 ( - 3 )}

Separate the solutions

t_{1} = \frac{- ( - 6 ) + 4 6}{2 ( - 3 )}, t_{2} = \frac{- ( - 6 ) - 4 6}{2 ( - 3 )}

t = \frac{- ( - 6 ) + 4 6}{2 ( - 3 )} : - \frac{3 + 2 6}{3}

t = \frac{- ( - 6 ) - 4 6}{2 ( - 3 )} : \frac{2 6 - 3}{3}

The solutions to the quadratic equation are:

t = - \frac{3 + 2 6}{3}, t = \frac{2 6 - 3}{3}

x^{2} + 7 x = 2 x + 14

x^{2} - 16 x + 51 = 0

\frac{15 i}{2 + i}

x^{2} > 16 x + 36

2 x^{3} - 3 x^{2} + 32 x + 17

What are the solutions to the equation -3t(t+2)=-5 ?
The solutions to the equation -3t(t+2)=-5 are t=-(3+2sqrt(6))/3 ,t=(2sqrt(6)-3)/3
Find the zeros of -3t(t+2)=-5
The zeros of -3t(t+2)=-5 are t=-(3+2sqrt(6))/3 ,t=(2sqrt(6)-3)/3