7=3/4n+n

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

7=3/4n+n

We move all terms to the left:

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


Domain of the equation: 4n+n)!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-n-3/4n+7=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -4; b = 28; c = -3;
Δ = b2-4ac
Δ = 282-4·(-4)·(-3)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{46}}{2*-4}=\frac{-28-4\sqrt{46}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{46}}{2*-4}=\frac{-28+4\sqrt{46}}{-8}
$