-6n^2=-17+11n

Solution for -6n^2=-17+11n equation:

-6n^2=-17+11n

We move all terms to the left:

-6n^2-(-17+11n)=0

We add all the numbers together, and all the variables

-6n^2-(11n-17)=0

We get rid of parentheses

-6n^2-11n+17=0

a = -6; b = -11; c = +17;
Δ = b2-4ac
Δ = -112-4·(-6)·17
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-23}{2*-6}=\frac{-12}{-12}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+23}{2*-6}=\frac{34}{-12}
=-2+5/6
$