5n^2-102n+360=0

Solution for 5n^2-102n+360=0 equation:

5n^2-102n+360=0

a = 5; b = -102; c = +360;
Δ = b2-4ac
Δ = -1022-4·5·360
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-6\sqrt{89}}{2*5}=\frac{102-6\sqrt{89}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+6\sqrt{89}}{2*5}=\frac{102+6\sqrt{89}}{10}
$