6k^2-70=k

Solution for 6k^2-70=k equation:

6k^2-70=k

We move all terms to the left:

6k^2-70-(k)=0

We add all the numbers together, and all the variables

6k^2-1k-70=0

a = 6; b = -1; c = -70;
Δ = b2-4ac
Δ = -12-4·6·(-70)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-41}{2*6}=\frac{-40}{12}
=-3+1/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+41}{2*6}=\frac{42}{12}
=3+1/2
$