(n+2)(n-7)/2=35

Solution for (n+2)(n-7)/2=35 equation:

(n+2)(n-7)/2=35

We move all terms to the left:

(n+2)(n-7)/2-(35)=0

We multiply parentheses ..

(+n^2-7n+2n-14)/2-35=0

We multiply all the terms by the denominator


(+n^2-7n+2n-14)-35*2=0

We add all the numbers together, and all the variables

(+n^2-7n+2n-14)-70=0

We get rid of parentheses

n^2-7n+2n-14-70=0

We add all the numbers together, and all the variables

n^2-5n-84=0

a = 1; b = -5; c = -84;
Δ = b2-4ac
Δ = -52-4·1·(-84)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*1}=\frac{-14}{2}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*1}=\frac{24}{2}
=12
$