85=2n^2-2n+1

Solution for 85=2n^2-2n+1 equation:

85=2n^2-2n+1

We move all terms to the left:

85-(2n^2-2n+1)=0

We get rid of parentheses

-2n^2+2n-1+85=0

We add all the numbers together, and all the variables

-2n^2+2n+84=0

a = -2; b = 2; c = +84;
Δ = b2-4ac
Δ = 22-4·(-2)·84
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-26}{2*-2}=\frac{-28}{-4}
=+7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+26}{2*-2}=\frac{24}{-4}
=-6
$