n(8n-1)=5040

Solution for n(8n-1)=5040 equation:

n(8n-1)=5040

We move all terms to the left:

n(8n-1)-(5040)=0

We multiply parentheses

8n^2-1n-5040=0

a = 8; b = -1; c = -5040;
Δ = b2-4ac
Δ = -12-4·8·(-5040)
Δ = 161281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{161281}}{2*8}=\frac{1-\sqrt{161281}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{161281}}{2*8}=\frac{1+\sqrt{161281}}{16}
$