What are the solutions to the equation 2d^2-8d+19=6d ?

The solutions to the equation 2d^2-8d+19=6d are d=(7+sqrt(11))/2 ,d=(7-sqrt(11))/2

Find the zeros of 2d^2-8d+19=6d

The zeros of 2d^2-8d+19=6d are d=(7+sqrt(11))/2 ,d=(7-sqrt(11))/2

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2 d^{2} - 8 d + 19 = 6 d

d = \frac{7 + 11}{2}, d = \frac{7 - 11}{2}

Decimal Notation

d = 5.15831 \dots, d = 1.84168 \dots

Solution steps

2 d^{2} - 8 d + 19 = 6 d

Move

6 d

to the left side

2 d^{2} - 14 d + 19 = 0

Solve with the quadratic formula

d_{1, 2} = \frac{- ( - 14 ) \pm ( - 14 ) ^{2} - 4 \cdot 2 \cdot 19}{2 \cdot 2}

(- 14)^{2} - 4 \cdot 2 \cdot 19 = 211

d_{1, 2} = \frac{- ( - 14 ) \pm 2 11}{2 \cdot 2}

Separate the solutions

d_{1} = \frac{- ( - 14 ) + 2 11}{2 \cdot 2}, d_{2} = \frac{- ( - 14 ) - 2 11}{2 \cdot 2}

d = \frac{- ( - 14 ) + 2 11}{2 \cdot 2} : \frac{7 + 11}{2}

d = \frac{- ( - 14 ) - 2 11}{2 \cdot 2} : \frac{7 - 11}{2}

The solutions to the quadratic equation are:

d = \frac{7 + 11}{2}, d = \frac{7 - 11}{2}

12 x^{2} + 12 x - 6 = 0

2 x^{2} - 5 x = - 5

x^{2} - 5 x + 9 = 3

x^{2} + 4 x - 3

x^{2} - 6 = - 5 x

What are the solutions to the equation 2d^2-8d+19=6d ?
The solutions to the equation 2d^2-8d+19=6d are d=(7+sqrt(11))/2 ,d=(7-sqrt(11))/2
Find the zeros of 2d^2-8d+19=6d
The zeros of 2d^2-8d+19=6d are d=(7+sqrt(11))/2 ,d=(7-sqrt(11))/2