What are the solutions to the equation 3p^2-14p+19=4p ?

The solutions to the equation 3p^2-14p+19=4p are p=(9+2sqrt(6))/3 ,p=(9-2sqrt(6))/3

Find the zeros of 3p^2-14p+19=4p

The zeros of 3p^2-14p+19=4p are p=(9+2sqrt(6))/3 ,p=(9-2sqrt(6))/3

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3 p^{2} - 14 p + 19 = 4 p

p = \frac{9 + 2 6}{3}, p = \frac{9 - 2 6}{3}

Decimal Notation

p = 4.63299 \dots, p = 1.36700 \dots

Solution steps

3 p^{2} - 14 p + 19 = 4 p

Move

4 p

to the left side

3 p^{2} - 18 p + 19 = 0

Solve with the quadratic formula

p_{1, 2} = \frac{- ( - 18 ) \pm ( - 18 ) ^{2} - 4 \cdot 3 \cdot 19}{2 \cdot 3}

(- 18)^{2} - 4 \cdot 3 \cdot 19 = 46

p_{1, 2} = \frac{- ( - 18 ) \pm 4 6}{2 \cdot 3}

Separate the solutions

p_{1} = \frac{- ( - 18 ) + 4 6}{2 \cdot 3}, p_{2} = \frac{- ( - 18 ) - 4 6}{2 \cdot 3}

p = \frac{- ( - 18 ) + 4 6}{2 \cdot 3} : \frac{9 + 2 6}{3}

p = \frac{- ( - 18 ) - 4 6}{2 \cdot 3} : \frac{9 - 2 6}{3}

The solutions to the quadratic equation are:

p = \frac{9 + 2 6}{3}, p = \frac{9 - 2 6}{3}

3 x^{2} + 7 x = - 9

25 (x^{2} - 1) + 12 = - 12

x^{2} - 24 x + 23 = 0

- 2 = \frac{1}{3} x^{2} + 25

(19 - 2 x) (15 - 2 x) = 77

What are the solutions to the equation 3p^2-14p+19=4p ?
The solutions to the equation 3p^2-14p+19=4p are p=(9+2sqrt(6))/3 ,p=(9-2sqrt(6))/3
Find the zeros of 3p^2-14p+19=4p
The zeros of 3p^2-14p+19=4p are p=(9+2sqrt(6))/3 ,p=(9-2sqrt(6))/3