6k^2=-252+78k

Solution for 6k^2=-252+78k equation:

6k^2=-252+78k

We move all terms to the left:

6k^2-(-252+78k)=0

We add all the numbers together, and all the variables

6k^2-(78k-252)=0

We get rid of parentheses

6k^2-78k+252=0

a = 6; b = -78; c = +252;
Δ = b2-4ac
Δ = -782-4·6·252
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-6}{2*6}=\frac{72}{12}
=6
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+6}{2*6}=\frac{84}{12}
=7
$