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

The solutions to the equation 6x+3=2x^2 are x=(3+sqrt(15))/2 ,x=(3-sqrt(15))/2

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

The zeros of 6x+3=2x^2 are x=(3+sqrt(15))/2 ,x=(3-sqrt(15))/2

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6 x + 3 = 2 x^{2}

x = \frac{3 + 15}{2}, x = \frac{3 - 15}{2}

Solution steps

6 x + 3 = 2 x^{2}

Switch sides

2 x^{2} = 6 x + 3

Move

3

to the left side

2 x^{2} - 3 = 6 x

Move

6 x

to the left side

2 x^{2} - 3 - 6 x = 0

Write in the standard form

a x^{2} + b x + c = 0

2 x^{2} - 6 x - 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 2 ( - 3 )}{2 \cdot 2}

(- 6)^{2} - 4 \cdot 2 (- 3) = 215

x_{1, 2} = \frac{- ( - 6 ) \pm 2 15}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 15}{2 \cdot 2}, x_{2} = \frac{- ( - 6 ) - 2 15}{2 \cdot 2}

x = \frac{- ( - 6 ) + 2 15}{2 \cdot 2} : \frac{3 + 15}{2}

x = \frac{- ( - 6 ) - 2 15}{2 \cdot 2} : \frac{3 - 15}{2}

The solutions to the quadratic equation are:

x = \frac{3 + 15}{2}, x = \frac{3 - 15}{2}

x^{2} - \frac{4}{5} x - 1

z^{2} - 2 z

z^{2} + 3 z - 7 = z

x^{2} + 2 x - 8 = 0

3 x^{2} - 7 = 5

What are the solutions to the equation 6x+3=2x^2 ?
The solutions to the equation 6x+3=2x^2 are x=(3+sqrt(15))/2 ,x=(3-sqrt(15))/2
Find the zeros of 6x+3=2x^2
The zeros of 6x+3=2x^2 are x=(3+sqrt(15))/2 ,x=(3-sqrt(15))/2