5n*n=8n+21

Solution for 5n*n=8n+21 equation:

5n*n=8n+21

We move all terms to the left:

5n*n-(8n+21)=0

Wy multiply elements

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

We get rid of parentheses

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{-14}{10}
=-1+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+22}{2*5}=\frac{30}{10}
=3
$