Question

X=6/(2x-8)

Answer 1

x=6/(2x-8)     

x(2x-8)=6

2x^2-8x-6=0 |^2

x^2-4x-3=0

D=(-4)^2-4*1*(-3)=16+12=28

x1=(4+2sqrt{7})/2=2+sqrt{7}

x2=(4-2sqrt{7})/2=2-sqrt{7}

Answer 2

To solve for x in this equation:

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X = 6 / (2x - 8)

We can start by cross-multiplying:

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X * (2x - 8) = 6

Expanding the left-hand side gives:

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2x^2 - 8X = 6

Moving all terms to one side, we get:

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2x^2 - 8X - 6 = 0

Dividing both sides by 2 gives:

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x^2 - 4x - 3 = 0

Now we can use the quadratic formula:

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x = (-b ± sqrt(b^2 - 4ac)) / 2a

Where a = 1, b = -4, and c = -3.

Plugging these values into the formula, we get:

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x = (-(-4) ± sqrt((-4)^2 - 4(1)(-3))) / 2(1)
x = (4 ± sqrt(28)) / 2

Simplifying the square root gives:

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x = (4 ± 2sqrt(7)) / 2

Simplifying further gives:

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x = 2 ± sqrt(7)

Therefore, the solutions to the equation are:

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x = 2 + sqrt(7)
x = 2 - sqrt(7)

Note that we need to check if these solutions satisfy the original equation. If we plug each solution back into the original equation, we can confirm that they are valid.