What are the solutions to the equation 3x^2-6x-7=x^2+3x-x(x+1)+3 ?

The solutions to the equation 3x^2-6x-7=x^2+3x-x(x+1)+3 are x=(4+sqrt(46))/3 ,x=(4-sqrt(46))/3

Find the zeros of 3x^2-6x-7=x^2+3x-x(x+1)+3

The zeros of 3x^2-6x-7=x^2+3x-x(x+1)+3 are x=(4+sqrt(46))/3 ,x=(4-sqrt(46))/3

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3 x^{2} - 6 x - 7 = x^{2} + 3 x - x (x + 1) + 3

x = \frac{4 + 46}{3}, x = \frac{4 - 46}{3}

Solution steps

3 x^{2} - 6 x - 7 = x^{2} + 3 x - x (x + 1) + 3

Expand

x^{2} + 3 x - x (x + 1) + 3 : 2 x + 3

3 x^{2} - 6 x - 7 = 2 x + 3

Move

3

to the left side

3 x^{2} - 6 x - 10 = 2 x

Move

2 x

to the left side

3 x^{2} - 8 x - 10 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 3 ( - 10 )}{2 \cdot 3}

(- 8)^{2} - 4 \cdot 3 (- 10) = 246

x_{1, 2} = \frac{- ( - 8 ) \pm 2 46}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 2 46}{2 \cdot 3}, x_{2} = \frac{- ( - 8 ) - 2 46}{2 \cdot 3}

x = \frac{- ( - 8 ) + 2 46}{2 \cdot 3} : \frac{4 + 46}{3}

x = \frac{- ( - 8 ) - 2 46}{2 \cdot 3} : \frac{4 - 46}{3}

The solutions to the quadratic equation are:

x = \frac{4 + 46}{3}, x = \frac{4 - 46}{3}

x, 3 x^{2} - 3 y^{2} = 0

2 x^{2} - 2 x = x^{2} + 2 x + 1

3 (x + 2)^{2} + 4 = 40

3 x (2 x + 9) = 10 x

4 x^{2} - 11 x = 7

What are the solutions to the equation 3x^2-6x-7=x^2+3x-x(x+1)+3 ?
The solutions to the equation 3x^2-6x-7=x^2+3x-x(x+1)+3 are x=(4+sqrt(46))/3 ,x=(4-sqrt(46))/3
Find the zeros of 3x^2-6x-7=x^2+3x-x(x+1)+3
The zeros of 3x^2-6x-7=x^2+3x-x(x+1)+3 are x=(4+sqrt(46))/3 ,x=(4-sqrt(46))/3