8n(3n+5)=25

Solution for 8n(3n+5)=25 equation:

8n(3n+5)=25

We move all terms to the left:

8n(3n+5)-(25)=0

We multiply parentheses

24n^2+40n-25=0

a = 24; b = 40; c = -25;
Δ = b2-4ac
Δ = 402-4·24·(-25)
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20\sqrt{10}}{2*24}=\frac{-40-20\sqrt{10}}{48}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20\sqrt{10}}{2*24}=\frac{-40+20\sqrt{10}}{48}
$