3/5n+75=50+2n

Solution for 3/5n+75=50+2n equation:

3/5n+75=50+2n

We move all terms to the left:

3/5n+75-(50+2n)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

3/5n-(2n+50)+75=0

We get rid of parentheses

3/5n-2n-50+75=0

We multiply all the terms by the denominator


-2n*5n-50*5n+75*5n+3=0

Wy multiply elements

-10n^2-250n+375n+3=0

We add all the numbers together, and all the variables

-10n^2+125n+3=0

a = -10; b = 125; c = +3;
Δ = b2-4ac
Δ = 1252-4·(-10)·3
Δ = 15745
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{-(125)-\sqrt{15745}}{2*-10}=\frac{-125-\sqrt{15745}}{-20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+\sqrt{15745}}{2*-10}=\frac{-125+\sqrt{15745}}{-20}
$