5n^2-16=38n

Solution for 5n^2-16=38n equation:

5n^2-16=38n

We move all terms to the left:

5n^2-16-(38n)=0

a = 5; b = -38; c = -16;
Δ = b2-4ac
Δ = -382-4·5·(-16)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-42}{2*5}=\frac{-4}{10}
=-2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+42}{2*5}=\frac{80}{10}
=8
$