n=3/4n+7

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

n=3/4n+7

We move all terms to the left:

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


Domain of the equation: 4n+7)!=0

n∈R


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 = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-8\sqrt{13}}{2*4}=\frac{28-8\sqrt{13}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+8\sqrt{13}}{2*4}=\frac{28+8\sqrt{13}}{8}
$