9n^2+10n=91n

Solution for 9n^2+10n=91n equation:

9n^2+10n=91n

We move all terms to the left:

9n^2+10n-(91n)=0

We add all the numbers together, and all the variables

9n^2-81n=0

a = 9; b = -81; c = 0;
Δ = b2-4ac
Δ = -812-4·9·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-81}{2*9}=\frac{0}{18}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+81}{2*9}=\frac{162}{18}
=9
$