n*n+111n-1026=0

Solution for n*n+111n-1026=0 equation:

n*n+111n-1026=0

We add all the numbers together, and all the variables

111n+n*n-1026=0

Wy multiply elements

n^2+111n-1026=0

a = 1; b = 111; c = -1026;
Δ = b2-4ac
Δ = 1112-4·1·(-1026)
Δ = 16425
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:

$\sqrt{\Delta}=\sqrt{16425}=\sqrt{225*73}=\sqrt{225}*\sqrt{73}=15\sqrt{73}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(111)-15\sqrt{73}}{2*1}=\frac{-111-15\sqrt{73}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(111)+15\sqrt{73}}{2*1}=\frac{-111+15\sqrt{73}}{2}
$