What are the solutions to the equation r^2-r-14=2r ?

The solutions to the equation r^2-r-14=2r are r=(3+sqrt(65))/2 ,r=(3-sqrt(65))/2

Find the zeros of r^2-r-14=2r

The zeros of r^2-r-14=2r are r=(3+sqrt(65))/2 ,r=(3-sqrt(65))/2

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r^{2} - r - 14 = 2 r

r = \frac{3 + 65}{2}, r = \frac{3 - 65}{2}

Decimal Notation

r = 5.53112 \dots, r = - 2.53112 \dots

Solution steps

r^{2} - r - 14 = 2 r

Move

2 r

to the left side

r^{2} - 3 r - 14 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot ( - 14 )}{2 \cdot 1}

(- 3)^{2} - 4 \cdot 1 \cdot (- 14) = 65

r_{1, 2} = \frac{- ( - 3 ) \pm 65}{2 \cdot 1}

Separate the solutions

r_{1} = \frac{- ( - 3 ) + 65}{2 \cdot 1}, r_{2} = \frac{- ( - 3 ) - 65}{2 \cdot 1}

r = \frac{- ( - 3 ) + 65}{2 \cdot 1} : \frac{3 + 65}{2}

r = \frac{- ( - 3 ) - 65}{2 \cdot 1} : \frac{3 - 65}{2}

The solutions to the quadratic equation are:

r = \frac{3 + 65}{2}, r = \frac{3 - 65}{2}

14 x^{2} - 36 x + 16 = 0

2 x^{2} + 36 x + 34 = 0

x^{2} = x + 90

- 6 x + 3 x^{2} = 0

x^{2} = x + 30

What are the solutions to the equation r^2-r-14=2r ?
The solutions to the equation r^2-r-14=2r are r=(3+sqrt(65))/2 ,r=(3-sqrt(65))/2
Find the zeros of r^2-r-14=2r
The zeros of r^2-r-14=2r are r=(3+sqrt(65))/2 ,r=(3-sqrt(65))/2