What are the solutions to the equation 6n^2-6n+3=4n^2 ?

The solutions to the equation 6n^2-6n+3=4n^2 are n=(3+sqrt(3))/2 ,n=(3-sqrt(3))/2

Find the zeros of 6n^2-6n+3=4n^2

The zeros of 6n^2-6n+3=4n^2 are n=(3+sqrt(3))/2 ,n=(3-sqrt(3))/2

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6 n^{2} - 6 n + 3 = 4 n^{2}

n = \frac{3 + 3}{2}, n = \frac{3 - 3}{2}

Decimal Notation

n = 2.36602 \dots, n = 0.63397 \dots

Solution steps

6 n^{2} - 6 n + 3 = 4 n^{2}

Move

4 n^{2}

to the left side

2 n^{2} - 6 n + 3 = 0

Solve with the quadratic formula

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

(- 6)^{2} - 4 \cdot 2 \cdot 3 = 23

n_{1, 2} = \frac{- ( - 6 ) \pm 2 3}{2 \cdot 2}

Separate the solutions

n_{1} = \frac{- ( - 6 ) + 2 3}{2 \cdot 2}, n_{2} = \frac{- ( - 6 ) - 2 3}{2 \cdot 2}

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

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

The solutions to the quadratic equation are:

n = \frac{3 + 3}{2}, n = \frac{3 - 3}{2}

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

x^{2} = (x - 8)^{2} + (x - 1)^{2}

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

4 (x + 2) (x + 3) - 6 x = 12

x^{2} - 6 x - 3

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