(-6n-13n^2)+(-3n+9n^2)=0

Solution for (-6n-13n^2)+(-3n+9n^2)=0 equation:

(-6n-13n^2)+(-3n+9n^2)=0

We get rid of parentheses

-13n^2+9n^2-6n-3n=0

We add all the numbers together, and all the variables

-4n^2-9n=0

a = -4; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-4)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-4}=\frac{0}{-8}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-4}=\frac{18}{-8}
=-2+1/4
$