8n(5n+13)=7

Solution for 8n(5n+13)=7 equation:

8n(5n+13)=7

We move all terms to the left:

8n(5n+13)-(7)=0

We multiply parentheses

40n^2+104n-7=0

a = 40; b = 104; c = -7;
Δ = b2-4ac
Δ = 1042-4·40·(-7)
Δ = 11936
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:

$\sqrt{\Delta}=\sqrt{11936}=\sqrt{16*746}=\sqrt{16}*\sqrt{746}=4\sqrt{746}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-4\sqrt{746}}{2*40}=\frac{-104-4\sqrt{746}}{80}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+4\sqrt{746}}{2*40}=\frac{-104+4\sqrt{746}}{80}
$