What are the solutions to the equation x^2-2x+3=2x+6 ?

The solutions to the equation x^2-2x+3=2x+6 are x=2+sqrt(7),x=2-sqrt(7)

Find the zeros of x^2-2x+3=2x+6

The zeros of x^2-2x+3=2x+6 are x=2+sqrt(7),x=2-sqrt(7)

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

x = 2 + 7, x = 2 - 7

Decimal Notation

x = 4.64575 \dots, x = - 0.64575 \dots

Solution steps

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

Move

6

to the left side

x^{2} - 2 x - 3 = 2 x

Move

2 x

to the left side

x^{2} - 4 x - 3 = 0

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 1 \cdot (- 3) = 27

x_{1, 2} = \frac{- ( - 4 ) \pm 2 7}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 7}{2 \cdot 1}, x_{2} = \frac{- ( - 4 ) - 2 7}{2 \cdot 1}

x = \frac{- ( - 4 ) + 2 7}{2 \cdot 1} : 2 + 7

x = \frac{- ( - 4 ) - 2 7}{2 \cdot 1} : 2 - 7

The solutions to the quadratic equation are:

x = 2 + 7, x = 2 - 7

5 (x^{2} + 2) = 7 (x + 3)

x^{2} - 7 x + 10 = 0

6 x^{2} + x = 2

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

5 x^{2} + 2 x - 5 = 0

What are the solutions to the equation x^2-2x+3=2x+6 ?
The solutions to the equation x^2-2x+3=2x+6 are x=2+sqrt(7),x=2-sqrt(7)
Find the zeros of x^2-2x+3=2x+6
The zeros of x^2-2x+3=2x+6 are x=2+sqrt(7),x=2-sqrt(7)