0=10n^2+11n-21

Solution for 0=10n^2+11n-21 equation:

0=10n^2+11n-21

We move all terms to the left:

0-(10n^2+11n-21)=0

We add all the numbers together, and all the variables

-(10n^2+11n-21)=0

We get rid of parentheses

-10n^2-11n+21=0

a = -10; b = -11; c = +21;
Δ = b2-4ac
Δ = -112-4·(-10)·21
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-31}{2*-10}=\frac{-20}{-20}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+31}{2*-10}=\frac{42}{-20}
=-2+1/10
$