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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(3(n-1)5n), so:

3(n-1)5n

We multiply parentheses

15n^2-15n

Back to the equation:

-(15n^2-15n)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-15n^2-2n+15n+5=0

We add all the numbers together, and all the variables

-15n^2+13n+5=0

a = -15; b = 13; c = +5;
Δ = b2-4ac
Δ = 132-4·(-15)·5
Δ = 469
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{-(13)-\sqrt{469}}{2*-15}=\frac{-13-\sqrt{469}}{-30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{469}}{2*-15}=\frac{-13+\sqrt{469}}{-30}
$