What are the solutions to the equation -5x^2+x+6=x^2-3x ?

The solutions to the equation -5x^2+x+6=x^2-3x are x=-(-1+sqrt(10))/3 ,x=(1+sqrt(10))/3

Find the zeros of -5x^2+x+6=x^2-3x

The zeros of -5x^2+x+6=x^2-3x are x=-(-1+sqrt(10))/3 ,x=(1+sqrt(10))/3

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

x = - \frac{- 1 + 10}{3}, x = \frac{1 + 10}{3}

Decimal Notation

x = - 0.72075 \dots, x = 1.38742 \dots

Solution steps

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

Move

3 x

to the left side

- 5 x^{2} + 4 x + 6 = x^{2}

Move

x^{2}

to the left side

- 6 x^{2} + 4 x + 6 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 ( - 6 ) \cdot 6}{2 ( - 6 )}

4^{2} - 4 (- 6) \cdot 6 = 410

x_{1, 2} = \frac{- 4 \pm 4 10}{2 ( - 6 )}

Separate the solutions

x_{1} = \frac{- 4 + 4 10}{2 ( - 6 )}, x_{2} = \frac{- 4 - 4 10}{2 ( - 6 )}

x = \frac{- 4 + 4 10}{2 ( - 6 )} : - \frac{- 1 + 10}{3}

x = \frac{- 4 - 4 10}{2 ( - 6 )} : \frac{1 + 10}{3}

The solutions to the quadratic equation are:

x = - \frac{- 1 + 10}{3}, x = \frac{1 + 10}{3}

6 x^{2} + 72 x - 170 = - 2

x^{2} - 32 x + 192 = 0

x^{2} - \frac{3}{2} x + \frac{1}{2} = 0

x^{2} + 100 x + 2500 = 0

x^{2} - 19 x = 0

What are the solutions to the equation -5x^2+x+6=x^2-3x ?
The solutions to the equation -5x^2+x+6=x^2-3x are x=-(-1+sqrt(10))/3 ,x=(1+sqrt(10))/3
Find the zeros of -5x^2+x+6=x^2-3x
The zeros of -5x^2+x+6=x^2-3x are x=-(-1+sqrt(10))/3 ,x=(1+sqrt(10))/3