-2n(n-12)+1=-2n+25

Solution for -2n(n-12)+1=-2n+25 equation:

-2n(n-12)+1=-2n+25

We move all terms to the left:

-2n(n-12)+1-(-2n+25)=0

We multiply parentheses

-2n^2+24n-(-2n+25)+1=0

We get rid of parentheses

-2n^2+24n+2n-25+1=0

We add all the numbers together, and all the variables

-2n^2+26n-24=0

a = -2; b = 26; c = -24;
Δ = b2-4ac
Δ = 262-4·(-2)·(-24)
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{-(26)-22}{2*-2}=\frac{-48}{-4}
=+12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+22}{2*-2}=\frac{-4}{-4}
=1
$