8=-4n+5n^2

Solution for 8=-4n+5n^2 equation:

8=-4n+5n^2

We move all terms to the left:

8-(-4n+5n^2)=0

We get rid of parentheses

-5n^2+4n+8=0

a = -5; b = 4; c = +8;
Δ = b2-4ac
Δ = 42-4·(-5)·8
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{11}}{2*-5}=\frac{-4-4\sqrt{11}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{11}}{2*-5}=\frac{-4+4\sqrt{11}}{-10}
$