36n^2-40n+8=0

Solution for 36n^2-40n+8=0 equation:

36n^2-40n+8=0

a = 36; b = -40; c = +8;
Δ = b2-4ac
Δ = -402-4·36·8
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{7}}{2*36}=\frac{40-8\sqrt{7}}{72}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{7}}{2*36}=\frac{40+8\sqrt{7}}{72}
$