3(n-1)5n+3=2n

Solution for 3(n-1)5n+3=2n equation:

3(n-1)5n+3=2n

We move all terms to the left:

3(n-1)5n+3-(2n)=0

We add all the numbers together, and all the variables

-2n+3(n-1)5n+3=0

We multiply parentheses

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

We add all the numbers together, and all the variables

15n^2-17n+3=0

a = 15; b = -17; c = +3;
Δ = b2-4ac
Δ = -172-4·15·3
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{109}}{2*15}=\frac{17-\sqrt{109}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{109}}{2*15}=\frac{17+\sqrt{109}}{30}
$