-5n(n+9)=-6n

Solution for -5n(n+9)=-6n equation:

-5n(n+9)=-6n

We move all terms to the left:

-5n(n+9)-(-6n)=0

We multiply parentheses

-5n^2-45n-(-6n)=0

We get rid of parentheses

-5n^2-45n+6n=0

We add all the numbers together, and all the variables

-5n^2-39n=0

a = -5; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·(-5)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*-5}=\frac{0}{-10}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*-5}=\frac{78}{-10}
=-7+4/5
$