5n^2-8=18n

Solution for 5n^2-8=18n equation:

5n^2-8=18n

We move all terms to the left:

5n^2-8-(18n)=0

a = 5; b = -18; c = -8;
Δ = b2-4ac
Δ = -182-4·5·(-8)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-22}{2*5}=\frac{-4}{10}
=-2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+22}{2*5}=\frac{40}{10}
=4
$