10n^2+30n=4n^2

Solution for 10n^2+30n=4n^2 equation:

10n^2+30n=4n^2

We move all terms to the left:

10n^2+30n-(4n^2)=0

determiningTheFunctionDomain
10n^2-4n^2+30n=0

We add all the numbers together, and all the variables

6n^2+30n=0

a = 6; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·6·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*6}=\frac{-60}{12}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*6}=\frac{0}{12}
=0
$