(n+10)(n-7)=0

Solution for (n+10)(n-7)=0 equation:

(n+10)(n-7)=0

We multiply parentheses ..

(+n^2-7n+10n-70)=0

We get rid of parentheses

n^2-7n+10n-70=0

We add all the numbers together, and all the variables

n^2+3n-70=0

a = 1; b = 3; c = -70;
Δ = b2-4ac
Δ = 32-4·1·(-70)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-17}{2*1}=\frac{-20}{2}
=-10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+17}{2*1}=\frac{14}{2}
=7
$