Which equation has the solutions x = (5 +- 2 \sqrt(7))/(3)? a:   3x2  – 5x  + 7 = 0b:   3x2  – 5x  – 1 = 0c: 3x2  – 10x  + 6 = 0d: 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

Iam thinking the answer is a.) knew