0.25n+3=1+0/75n

Solution for 0.25n+3=1+0/75n equation:

0.25n+3=1+0/75n

We move all terms to the left:

0.25n+3-(1+0/75n)=0


Domain of the equation: 75n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

0.25n-(0/75n+1)+3=0

We get rid of parentheses

0.25n-0/75n-1+3=0

We multiply all the terms by the denominator


(0.25n)*75n-1*75n+3*75n-0=0

We add all the numbers together, and all the variables

(+0.25n)*75n-1*75n+3*75n-0=0

We add all the numbers together, and all the variables

(+0.25n)*75n-1*75n+3*75n=0

We multiply parentheses

0n^2-1*75n+3*75n=0

Wy multiply elements

0n^2-75n+225n=0

We add all the numbers together, and all the variables

n^2+150n=0

a = 1; b = 150; c = 0;
Δ = b2-4ac
Δ = 1502-4·1·0
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-150}{2*1}=\frac{-300}{2}
=-150
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+150}{2*1}=\frac{0}{2}
=0
$