3k^2-7k=6

Solution for 3k^2-7k=6 equation:

3k^2-7k=6

We move all terms to the left:

3k^2-7k-(6)=0

a = 3; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·3·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*3}=\frac{-4}{6}
=-2/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*3}=\frac{18}{6}
=3
$