What are the solutions to the equation x^2-12x+51=2x+3x ?

The solutions to the equation x^2-12x+51=2x+3x are x=(17+sqrt(85))/2 ,x=(17-sqrt(85))/2

Find the zeros of x^2-12x+51=2x+3x

The zeros of x^2-12x+51=2x+3x are x=(17+sqrt(85))/2 ,x=(17-sqrt(85))/2

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x^{2} - 12 x + 51 = 2 x + 3 x

x = \frac{17 + 85}{2}, x = \frac{17 - 85}{2}

Decimal Notation

x = 13.10977 \dots, x = 3.89022 \dots

Solution steps

x^{2} - 12 x + 51 = 2 x + 3 x

Refine

x^{2} - 12 x + 51 = 5 x

Move

5 x

to the left side

x^{2} - 17 x + 51 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 17 ) \pm ( - 17 ) ^{2} - 4 \cdot 1 \cdot 51}{2 \cdot 1}

(- 17)^{2} - 4 \cdot 1 \cdot 51 = 85

x_{1, 2} = \frac{- ( - 17 ) \pm 85}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 17 ) + 85}{2 \cdot 1}, x_{2} = \frac{- ( - 17 ) - 85}{2 \cdot 1}

x = \frac{- ( - 17 ) + 85}{2 \cdot 1} : \frac{17 + 85}{2}

x = \frac{- ( - 17 ) - 85}{2 \cdot 1} : \frac{17 - 85}{2}

The solutions to the quadratic equation are:

x = \frac{17 + 85}{2}, x = \frac{17 - 85}{2}

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

x^{2} - 2 x + \frac{13}{4} = 0

b^{2} = 12

w^{2} - 7 w + 1 = 0

x^{2} + 14 x + 19 = - 2 x

What are the solutions to the equation x^2-12x+51=2x+3x ?
The solutions to the equation x^2-12x+51=2x+3x are x=(17+sqrt(85))/2 ,x=(17-sqrt(85))/2
Find the zeros of x^2-12x+51=2x+3x
The zeros of x^2-12x+51=2x+3x are x=(17+sqrt(85))/2 ,x=(17-sqrt(85))/2