What are the solutions to the equation 3t^2-12t+3=0 ?

The solutions to the equation 3t^2-12t+3=0 are t=2+sqrt(3),t=2-sqrt(3)

Find the zeros of 3t^2-12t+3=0

The zeros of 3t^2-12t+3=0 are t=2+sqrt(3),t=2-sqrt(3)

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3 t^{2} - 12 t + 3 = 0

t = 2 + 3, t = 2 - 3

Decimal Notation

t = 3.73205 \dots, t = 0.26794 \dots

Solution steps

3 t^{2} - 12 t + 3 = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 3 \cdot 3}{2 \cdot 3}

(- 12)^{2} - 4 \cdot 3 \cdot 3 = 63

t_{1, 2} = \frac{- ( - 12 ) \pm 6 3}{2 \cdot 3}

Separate the solutions

t_{1} = \frac{- ( - 12 ) + 6 3}{2 \cdot 3}, t_{2} = \frac{- ( - 12 ) - 6 3}{2 \cdot 3}

t = \frac{- ( - 12 ) + 6 3}{2 \cdot 3} : 2 + 3

t = \frac{- ( - 12 ) - 6 3}{2 \cdot 3} : 2 - 3

The solutions to the quadratic equation are:

t = 2 + 3, t = 2 - 3

x^{2} + 12 x + 31 = 0

∣ x + 1 ∣ + 8 = 3

2 x^{2} - 9 x = 18

U^{1} = [- 2]

5 x^{2} + 1 = 26

What are the solutions to the equation 3t^2-12t+3=0 ?
The solutions to the equation 3t^2-12t+3=0 are t=2+sqrt(3),t=2-sqrt(3)
Find the zeros of 3t^2-12t+3=0
The zeros of 3t^2-12t+3=0 are t=2+sqrt(3),t=2-sqrt(3)