3/4n+7=28-n

Solution for 3/4n+7=28-n equation:

3/4n+7=28-n

We move all terms to the left:

3/4n+7-(28-n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

3/4n-(-1n+28)+7=0

We get rid of parentheses

3/4n+1n-28+7=0

We multiply all the terms by the denominator


1n*4n-28*4n+7*4n+3=0

Wy multiply elements

4n^2-112n+28n+3=0

We add all the numbers together, and all the variables

4n^2-84n+3=0

a = 4; b = -84; c = +3;
Δ = b2-4ac
Δ = -842-4·4·3
Δ = 7008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7008}=\sqrt{16*438}=\sqrt{16}*\sqrt{438}=4\sqrt{438}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{438}}{2*4}=\frac{84-4\sqrt{438}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{438}}{2*4}=\frac{84+4\sqrt{438}}{8}
$