3k^2=7k+1=0

Solution for 3k^2=7k+1=0 equation:

3k^2=7k+1=0

We move all terms to the left:

3k^2-(7k+1)=0

We get rid of parentheses

3k^2-7k-1=0

a = 3; b = -7; c = -1;
Δ = b2-4ac
Δ = -72-4·3·(-1)
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{61}}{2*3}=\frac{7-\sqrt{61}}{6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{61}}{2*3}=\frac{7+\sqrt{61}}{6}
$