8n+21=5n^2

Solution for 8n+21=5n^2 equation:

8n+21=5n^2

We move all terms to the left:

8n+21-(5n^2)=0

determiningTheFunctionDomain
-5n^2+8n+21=0

a = -5; b = 8; c = +21;
Δ = b2-4ac
Δ = 82-4·(-5)·21
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{-(8)-22}{2*-5}=\frac{-30}{-10}
=+3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+22}{2*-5}=\frac{14}{-10}
=-1+2/5
$