3/4n+4=10,n

Solution for 3/4n+4=10,n equation:

3/4n+4=10.n

We move all terms to the left:

3/4n+4-(10.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-(+10.n)+4=0

We get rid of parentheses

3/4n-10.n+4=0

We multiply all the terms by the denominator


-(10.n)*4n+4*4n+3=0

We add all the numbers together, and all the variables

-(+10.n)*4n+4*4n+3=0

We multiply parentheses

-40n^2+4*4n+3=0

Wy multiply elements

-40n^2+16n+3=0

a = -40; b = 16; c = +3;
Δ = b2-4ac
Δ = 162-4·(-40)·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{-(16)-4\sqrt{46}}{2*-40}=\frac{-16-4\sqrt{46}}{-80}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{46}}{2*-40}=\frac{-16+4\sqrt{46}}{-80}
$