Which equation has the solutions x = (5 + - 2 / sqrt (7)) / (3) ?

A: 3x2 - 5x + 7 = 0

B: 3x2 - 5x - 1 = 0

C: 3x2 - 10x + 6 = 0

D: 3x2 - 10x - 1 = 0

Which equation has the solutions?

3x2 - 5x + 7 = 0 3x2 - 5x - 1 = 0 3x2 - 10x + 6 = 0 3x2 - 10x - 1 = 0

Recall the formula to find the solutions for an equation ax² + bx + c:

x₁₂ = ( - b + / - √ (b²-4ac)) / 2a

Since at the denominator of our solution we have 3, which is an odd number, therefore it cannot be 2a, but only a, we should use the formula:

x₁₂ = (-β + / - √ (β²-ac)) / a

Where β = b/2

Hence, the only options that have an even number as b coefficient are C and D.

Now, we need to find what values give √ (β² - ac) = 2√7 = √ (4·7) = √28:

C) √ (β² - ac) = √ (25 - 3·6) = √7

D) √ (β² - ac) = √ (25 - 3· (-1)) = √28

Hence, the correct answer is D) 3x² - 10x - 1 = 0