What are the solutions to the equation (t)=3t+4(t)^2 ?

The solutions to the equation (t)=3t+4(t)^2 are t=0,t=-1/2

Find the zeros of (t)=3t+4(t)^2

The zeros of (t)=3t+4(t)^2 are t=0,t=-1/2

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(t) = 3 t + 4 (t)^{2}

t = 0, t = - \frac{1}{2}

Solution steps

(t) = 3 t + 4 t^{2}

Refine

t = 3 t + 4 t^{2}

Switch sides

3 t + 4 t^{2} = t

Move

t

to the left side

4 t^{2} + 2 t = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 4 \cdot 0}{2 \cdot 4}

2^{2} - 4 \cdot 4 \cdot 0 = 2

t_{1, 2} = \frac{- 2 \pm 2}{2 \cdot 4}

Separate the solutions

t_{1} = \frac{- 2 + 2}{2 \cdot 4}, t_{2} = \frac{- 2 - 2}{2 \cdot 4}

t = \frac{- 2 + 2}{2 \cdot 4} : 0

t = \frac{- 2 - 2}{2 \cdot 4} : - \frac{1}{2}

The solutions to the quadratic equation are:

t = 0, t = - \frac{1}{2}

5 x - 20 = 0

2 x + \frac{x - 3}{2} = \frac{x - 3}{4}

81 s^{2} + 126 s = - 49

5 \leq 3 x - 4 \leq 14

- 55

What are the solutions to the equation (t)=3t+4(t)^2 ?
The solutions to the equation (t)=3t+4(t)^2 are t=0,t=-1/2
Find the zeros of (t)=3t+4(t)^2
The zeros of (t)=3t+4(t)^2 are t=0,t=-1/2