3(-n+4)5n=2n

Solution for 3(-n+4)5n=2n equation:

3(-n+4)5n=2n

We move all terms to the left:

3(-n+4)5n-(2n)=0

We add all the numbers together, and all the variables

3(-1n+4)5n-2n=0

We add all the numbers together, and all the variables

-2n+3(-1n+4)5n=0

We multiply parentheses

-15n^2-2n+60n=0

We add all the numbers together, and all the variables

-15n^2+58n=0

a = -15; b = 58; c = 0;
Δ = b2-4ac
Δ = 582-4·(-15)·0
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-58}{2*-15}=\frac{-116}{-30}
=3+13/15
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+58}{2*-15}=\frac{0}{-30}
=0
$