6n2-15n=3n

Solution for 6n2-15n=3n equation:

6n^2-15n=3n

We move all terms to the left:

6n^2-15n-(3n)=0

We add all the numbers together, and all the variables

6n^2-18n=0

a = 6; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·6·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*6}=\frac{0}{12}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*6}=\frac{36}{12}
=3
$