7(3k-2)13k=82

Solution for 7(3k-2)13k=82 equation:

7(3k-2)13k=82

We move all terms to the left:

7(3k-2)13k-(82)=0

We multiply parentheses

273k^2-182k-82=0

a = 273; b = -182; c = -82;
Δ = b2-4ac
Δ = -1822-4·273·(-82)
Δ = 122668
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{122668}=\sqrt{4*30667}=\sqrt{4}*\sqrt{30667}=2\sqrt{30667}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-182)-2\sqrt{30667}}{2*273}=\frac{182-2\sqrt{30667}}{546}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-182)+2\sqrt{30667}}{2*273}=\frac{182+2\sqrt{30667}}{546}
$