2-15n=5n(-3n+2)

Solution for 2-15n=5n(-3n+2) equation:

2-15n=5n(-3n+2)

We move all terms to the left:

2-15n-(5n(-3n+2))=0


We calculate terms in parentheses: -(5n(-3n+2)), so:

5n(-3n+2)

We multiply parentheses

-15n^2+10n

Back to the equation:

-(-15n^2+10n)


We get rid of parentheses

15n^2-10n-15n+2=0

We add all the numbers together, and all the variables

15n^2-25n+2=0

a = 15; b = -25; c = +2;
Δ = b2-4ac
Δ = -252-4·15·2
Δ = 505
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{-(-25)-\sqrt{505}}{2*15}=\frac{25-\sqrt{505}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{505}}{2*15}=\frac{25+\sqrt{505}}{30}
$