What are the solutions to the equation 8=3t^2-5t+1 ?

The solutions to the equation 8=3t^2-5t+1 are t=(5+sqrt(109))/6 ,t=(5-sqrt(109))/6

Find the zeros of 8=3t^2-5t+1

The zeros of 8=3t^2-5t+1 are t=(5+sqrt(109))/6 ,t=(5-sqrt(109))/6

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8 = 3 t^{2} - 5 t + 1

t = \frac{5 + 109}{6}, t = \frac{5 - 109}{6}

Decimal Notation

t = 2.57338 \dots, t = - 0.90671 \dots

Solution steps

8 = 3 t^{2} - 5 t + 1

Switch sides

3 t^{2} - 5 t + 1 = 8

Move

8

to the left side

3 t^{2} - 5 t - 7 = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 3 ( - 7 )}{2 \cdot 3}

(- 5)^{2} - 4 \cdot 3 (- 7) = 109

t_{1, 2} = \frac{- ( - 5 ) \pm 109}{2 \cdot 3}

Separate the solutions

t_{1} = \frac{- ( - 5 ) + 109}{2 \cdot 3}, t_{2} = \frac{- ( - 5 ) - 109}{2 \cdot 3}

t = \frac{- ( - 5 ) + 109}{2 \cdot 3} : \frac{5 + 109}{6}

t = \frac{- ( - 5 ) - 109}{2 \cdot 3} : \frac{5 - 109}{6}

The solutions to the quadratic equation are:

t = \frac{5 + 109}{6}, t = \frac{5 - 109}{6}

2 r^{2} + 6 r = - 12 - 2 r

5 (x + 5)^{2} = 60

(x - 3)^{3} = x^{3} - 63

x^{2} + 16 x = 7

m^{2} - 4 m = 5

What are the solutions to the equation 8=3t^2-5t+1 ?
The solutions to the equation 8=3t^2-5t+1 are t=(5+sqrt(109))/6 ,t=(5-sqrt(109))/6
Find the zeros of 8=3t^2-5t+1
The zeros of 8=3t^2-5t+1 are t=(5+sqrt(109))/6 ,t=(5-sqrt(109))/6