sqrt(3x^2-5x+8)-sqrt(3x^2-5x-1)=1

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Solution for sqrt(3x^2-5x+8)-sqrt(3x^2-5x-1)=1 equation:


Simplifying
sqrt(3x2 + -5x + 8) + -1sqrt(3x2 + -5x + -1) = 1

Reorder the terms:
qrst(8 + -5x + 3x2) + -1sqrt(3x2 + -5x + -1) = 1
(8 * qrst + -5x * qrst + 3x2 * qrst) + -1sqrt(3x2 + -5x + -1) = 1
(8qrst + -5qrstx + 3qrstx2) + -1sqrt(3x2 + -5x + -1) = 1

Reorder the terms:
8qrst + -5qrstx + 3qrstx2 + -1qrst(-1 + -5x + 3x2) = 1
8qrst + -5qrstx + 3qrstx2 + (-1 * -1qrst + -5x * -1qrst + 3x2 * -1qrst) = 1
8qrst + -5qrstx + 3qrstx2 + (1qrst + 5qrstx + -3qrstx2) = 1

Reorder the terms:
8qrst + 1qrst + -5qrstx + 5qrstx + 3qrstx2 + -3qrstx2 = 1

Combine like terms: 8qrst + 1qrst = 9qrst
9qrst + -5qrstx + 5qrstx + 3qrstx2 + -3qrstx2 = 1

Combine like terms: -5qrstx + 5qrstx = 0
9qrst + 0 + 3qrstx2 + -3qrstx2 = 1
9qrst + 3qrstx2 + -3qrstx2 = 1

Combine like terms: 3qrstx2 + -3qrstx2 = 0
9qrst + 0 = 1
9qrst = 1

Solving
9qrst = 1

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Divide each side by '9rst'.
q = 0.1111111111r-1s-1t-1

Simplifying
q = 0.1111111111r-1s-1t-1

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