20n^2+11=891

Solution for 20n^2+11=891 equation:

20n^2+11=891

We move all terms to the left:

20n^2+11-(891)=0

We add all the numbers together, and all the variables

20n^2-880=0

a = 20; b = 0; c = -880;
Δ = b2-4ac
Δ = 02-4·20·(-880)
Δ = 70400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{70400}=\sqrt{6400*11}=\sqrt{6400}*\sqrt{11}=80\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{11}}{2*20}=\frac{0-80\sqrt{11}}{40}
=-\frac{80\sqrt{11}}{40}
=-2\sqrt{11}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{11}}{2*20}=\frac{0+80\sqrt{11}}{40}
=\frac{80\sqrt{11}}{40}
=2\sqrt{11}
$