n2+12n-85=0

Solution for n2+12n-85=0 equation:

n2+12n-85=0

We add all the numbers together, and all the variables

n^2+12n-85=0

a = 1; b = 12; c = -85;
Δ = b2-4ac
Δ = 122-4·1·(-85)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-22}{2*1}=\frac{-34}{2}
=-17
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+22}{2*1}=\frac{10}{2}
=5
$