What are the solutions to the equation 3t^2-12t+5=0 ?

The solutions to the equation 3t^2-12t+5=0 are t=(6+sqrt(21))/3 ,t=(6-sqrt(21))/3

Find the zeros of 3t^2-12t+5=0

The zeros of 3t^2-12t+5=0 are t=(6+sqrt(21))/3 ,t=(6-sqrt(21))/3

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3 t^{2} - 12 t + 5 = 0

t = \frac{6 + 21}{3}, t = \frac{6 - 21}{3}

Decimal Notation

t = 3.52752 \dots, t = 0.47247 \dots

Solution steps

3 t^{2} - 12 t + 5 = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 3 \cdot 5}{2 \cdot 3}

(- 12)^{2} - 4 \cdot 3 \cdot 5 = 221

t_{1, 2} = \frac{- ( - 12 ) \pm 2 21}{2 \cdot 3}

Separate the solutions

t_{1} = \frac{- ( - 12 ) + 2 21}{2 \cdot 3}, t_{2} = \frac{- ( - 12 ) - 2 21}{2 \cdot 3}

t = \frac{- ( - 12 ) + 2 21}{2 \cdot 3} : \frac{6 + 21}{3}

t = \frac{- ( - 12 ) - 2 21}{2 \cdot 3} : \frac{6 - 21}{3}

The solutions to the quadratic equation are:

t = \frac{6 + 21}{3}, t = \frac{6 - 21}{3}

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What are the solutions to the equation 3t^2-12t+5=0 ?
The solutions to the equation 3t^2-12t+5=0 are t=(6+sqrt(21))/3 ,t=(6-sqrt(21))/3
Find the zeros of 3t^2-12t+5=0
The zeros of 3t^2-12t+5=0 are t=(6+sqrt(21))/3 ,t=(6-sqrt(21))/3