Answer:
Option d is correct.
Step-by-step explanation:
We have bee given the solution which is:
[tex]x=\frac{5\pm2\sqrt{7}}{3}[/tex]
Using:[tex]D=b^2-4ac[/tex]
And then [tex]x=\frac{-b\pm\sqrt{D}}{2a}[/tex]
From the given equation we will check for D first and then we proceed because [tex]\sqrt{D}[/tex] is the initial step of the solution.
[tex]3x^2-10x-1=0[/tex]
Here, a=3,b= -10 and c=-1.
Substituting the values in the formula to get the solution.
[tex]D=(-10)^2-4(3)(-1)=112[/tex]
[tex]x=\frac{10\pm\sqrt{112}}{6}[/tex]
[tex]x=\frac{10\pm 4\sqrt{7}}{6}[/tex]
[tex]\Rightarrow x=\frac{5\pm2\sqrt{7}}{3}[/tex]
Option d is correct.
