What are the solutions to the equation 5n=2n^2-3 ?

The solutions to the equation 5n=2n^2-3 are n=3,n=-1/2

Find the zeros of 5n=2n^2-3

The zeros of 5n=2n^2-3 are n=3,n=-1/2

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5 n = 2 n^{2} - 3

n = 3, n = - \frac{1}{2}

Decimal

n = 3, n = - 0.5

Solution steps

5 n = 2 n^{2} - 3

Switch sides

2 n^{2} - 3 = 5 n

Move

5 n

to the left side

2 n^{2} - 3 - 5 n = 0

Write in the standard form

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

2 n^{2} - 5 n - 3 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 2 ( - 3 )}{2 \cdot 2}

(- 5)^{2} - 4 \cdot 2 (- 3) = 7

n_{1, 2} = \frac{- ( - 5 ) \pm 7}{2 \cdot 2}

Separate the solutions

n_{1} = \frac{- ( - 5 ) + 7}{2 \cdot 2}, n_{2} = \frac{- ( - 5 ) - 7}{2 \cdot 2}

n = \frac{- ( - 5 ) + 7}{2 \cdot 2} : 3

n = \frac{- ( - 5 ) - 7}{2 \cdot 2} : - \frac{1}{2}

The solutions to the quadratic equation are:

n = 3, n = - \frac{1}{2}

2 x^{2} + 32 x + 126 = 0

\frac{x ( x - 3 )}{2} = x

x^{2} - 9 x - 20 = - 6 x - 2

- 3 x^{2} + 72 = - 60

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

What are the solutions to the equation 5n=2n^2-3 ?
The solutions to the equation 5n=2n^2-3 are n=3,n=-1/2
Find the zeros of 5n=2n^2-3
The zeros of 5n=2n^2-3 are n=3,n=-1/2