k^2=15k-36

Solution for k^2=15k-36 equation:

k^2=15k-36

We move all terms to the left:

k^2-(15k-36)=0

We get rid of parentheses

k^2-15k+36=0

a = 1; b = -15; c = +36;
Δ = b2-4ac
Δ = -152-4·1·36
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*1}=\frac{6}{2}
=3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*1}=\frac{24}{2}
=12
$