8n(5n+13)=17

Solution for 8n(5n+13)=17 equation:

8n(5n+13)=17

We move all terms to the left:

8n(5n+13)-(17)=0

We multiply parentheses

40n^2+104n-17=0

a = 40; b = 104; c = -17;
Δ = b2-4ac
Δ = 1042-4·40·(-17)
Δ = 13536
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:

$\sqrt{\Delta}=\sqrt{13536}=\sqrt{144*94}=\sqrt{144}*\sqrt{94}=12\sqrt{94}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-12\sqrt{94}}{2*40}=\frac{-104-12\sqrt{94}}{80}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+12\sqrt{94}}{2*40}=\frac{-104+12\sqrt{94}}{80}
$