(2n+17)(n-8)=0

Solution for (2n+17)(n-8)=0 equation:

(2n+17)(n-8)=0

We multiply parentheses ..

(+2n^2-16n+17n-136)=0

We get rid of parentheses

2n^2-16n+17n-136=0

We add all the numbers together, and all the variables

2n^2+n-136=0

a = 2; b = 1; c = -136;
Δ = b2-4ac
Δ = 12-4·2·(-136)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-33}{2*2}=\frac{-34}{4}
=-8+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+33}{2*2}=\frac{32}{4}
=8
$