n(8n-7)=8481

Solution for n(8n-7)=8481 equation:

n(8n-7)=8481

We move all terms to the left:

n(8n-7)-(8481)=0

We multiply parentheses

8n^2-7n-8481=0

a = 8; b = -7; c = -8481;
Δ = b2-4ac
Δ = -72-4·8·(-8481)
Δ = 271441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{271441}=521$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-521}{2*8}=\frac{-514}{16}
=-32+1/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+521}{2*8}=\frac{528}{16}
=33
$