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
