5n^2-30n+36=0

Solution for 5n^2-30n+36=0 equation:

5n^2-30n+36=0

a = 5; b = -30; c = +36;
Δ = b2-4ac
Δ = -302-4·5·36
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{5}}{2*5}=\frac{30-6\sqrt{5}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{5}}{2*5}=\frac{30+6\sqrt{5}}{10}
$