What are the solutions to the equation ex=ex^2-6 ?

The solutions to the equation ex=ex^2-6 are x=(e+sqrt(e^2+24e))/(2e),x=(e-sqrt(e^2+24e))/(2e)

Find the zeros of ex=ex^2-6

The zeros of ex=ex^2-6 are x=(e+sqrt(e^2+24e))/(2e),x=(e-sqrt(e^2+24e))/(2e)

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e x = e x^{2} - 6

x = \frac{e + e ^{2} + 24 e}{2 e}, x = \frac{e - e ^{2} + 24 e}{2 e}

Decimal Notation

x = 2.06757 \dots, x = - 1.06757 \dots

Solution steps

e x = e x^{2} - 6

Switch sides

e x^{2} - 6 = e x

Move

e x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

(- e)^{2} - 4 e (- 6) = e^{2} + 24 e

x_{1, 2} = \frac{- ( - e ) \pm e ^{2} + 24 e}{2 e}

Separate the solutions

x_{1} = \frac{- ( - e ) + e ^{2} + 24 e}{2 e}, x_{2} = \frac{- ( - e ) - e ^{2} + 24 e}{2 e}

x = \frac{- ( - e ) + e ^{2} + 24 e}{2 e} : \frac{e + e ^{2} + 24 e}{2 e}

x = \frac{- ( - e ) - e ^{2} + 24 e}{2 e} : \frac{e - e ^{2} + 24 e}{2 e}

The solutions to the quadratic equation are:

x = \frac{e + e ^{2} + 24 e}{2 e}, x = \frac{e - e ^{2} + 24 e}{2 e}

x^{2} + 12 x = 6

- 7 x^{2} + 12 x = 10

- \frac{1}{8} x^{2} + x = 0

y, y^{2} = - 6 x^{2} + c

a x^{2} - (a - 5) x + 1 = 0, a

What are the solutions to the equation ex=ex^2-6 ?
The solutions to the equation ex=ex^2-6 are x=(e+sqrt(e^2+24e))/(2e),x=(e-sqrt(e^2+24e))/(2e)
Find the zeros of ex=ex^2-6
The zeros of ex=ex^2-6 are x=(e+sqrt(e^2+24e))/(2e),x=(e-sqrt(e^2+24e))/(2e)