q^2-54q+360=0

Solution for q^2-54q+360=0 equation:

q^2-54q+360=0

a = 1; b = -54; c = +360;
Δ = b2-4ac
Δ = -542-4·1·360
Δ = 1476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{41}}{2*1}=\frac{54-6\sqrt{41}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{41}}{2*1}=\frac{54+6\sqrt{41}}{2}
$