7n^2-32n+1=0

Solution for 7n^2-32n+1=0 equation:

7n^2-32n+1=0

a = 7; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·7·1
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{249}}{2*7}=\frac{32-2\sqrt{249}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{249}}{2*7}=\frac{32+2\sqrt{249}}{14}
$