k^2-21k+54=0

Solution for k^2-21k+54=0 equation:

k^2-21k+54=0

a = 1; b = -21; c = +54;
Δ = b2-4ac
Δ = -212-4·1·54
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-15}{2*1}=\frac{6}{2}
=3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+15}{2*1}=\frac{36}{2}
=18
$