-n2-17n-66=-34n

Solution for -n2-17n-66=-34n equation:

-n2-17n-66=-34n

We move all terms to the left:

-n2-17n-66-(-34n)=0

We add all the numbers together, and all the variables

-1n^2-17n-(-34n)-66=0

We get rid of parentheses

-1n^2-17n+34n-66=0

We add all the numbers together, and all the variables

-1n^2+17n-66=0

a = -1; b = 17; c = -66;
Δ = b2-4ac
Δ = 172-4·(-1)·(-66)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-5}{2*-1}=\frac{-22}{-2}
=+11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+5}{2*-1}=\frac{-12}{-2}
=+6
$