15n^2+7n=3+3n

Solution for 15n^2+7n=3+3n equation:

15n^2+7n=3+3n

We move all terms to the left:

15n^2+7n-(3+3n)=0

We add all the numbers together, and all the variables

15n^2+7n-(3n+3)=0

We get rid of parentheses

15n^2+7n-3n-3=0

We add all the numbers together, and all the variables

15n^2+4n-3=0

a = 15; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·15·(-3)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-14}{2*15}=\frac{-18}{30}
=-3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+14}{2*15}=\frac{10}{30}
=1/3
$