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

The solutions to the equation 3+2x^2-3x=7+6x are x=(9+sqrt(113))/4 ,x=(9-sqrt(113))/4

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

The zeros of 3+2x^2-3x=7+6x are x=(9+sqrt(113))/4 ,x=(9-sqrt(113))/4

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

x = \frac{9 + 113}{4}, x = \frac{9 - 113}{4}

Decimal Notation

x = 4.90753 \dots, x = - 0.40753 \dots

Solution steps

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

Move

6 x

to the left side

3 + 2 x^{2} - 9 x = 7

Move

7

to the left side

2 x^{2} - 9 x - 4 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 2 ( - 4 )}{2 \cdot 2}

(- 9)^{2} - 4 \cdot 2 (- 4) = 113

x_{1, 2} = \frac{- ( - 9 ) \pm 113}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 9 ) + 113}{2 \cdot 2}, x_{2} = \frac{- ( - 9 ) - 113}{2 \cdot 2}

x = \frac{- ( - 9 ) + 113}{2 \cdot 2} : \frac{9 + 113}{4}

x = \frac{- ( - 9 ) - 113}{2 \cdot 2} : \frac{9 - 113}{4}

The solutions to the quadratic equation are:

x = \frac{9 + 113}{4}, x = \frac{9 - 113}{4}

x^{2} + 16 x + 5 = 9

20 x^{2} - x - 1 = 0

3 x^{2} = 2 + x

8 m = m^{2} + 15

9 n^{2} - 14 = 0

What are the solutions to the equation 3+2x^2-3x=7+6x ?
The solutions to the equation 3+2x^2-3x=7+6x are x=(9+sqrt(113))/4 ,x=(9-sqrt(113))/4
Find the zeros of 3+2x^2-3x=7+6x
The zeros of 3+2x^2-3x=7+6x are x=(9+sqrt(113))/4 ,x=(9-sqrt(113))/4