n+3/4n=455

Solution for n+3/4n=455 equation:

n+3/4n=455

We move all terms to the left:

n+3/4n-(455)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We multiply all the terms by the denominator


n*4n-455*4n+3=0

Wy multiply elements

4n^2-1820n+3=0

a = 4; b = -1820; c = +3;
Δ = b2-4ac
Δ = -18202-4·4·3
Δ = 3312352
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:

$\sqrt{\Delta}=\sqrt{3312352}=\sqrt{16*207022}=\sqrt{16}*\sqrt{207022}=4\sqrt{207022}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1820)-4\sqrt{207022}}{2*4}=\frac{1820-4\sqrt{207022}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1820)+4\sqrt{207022}}{2*4}=\frac{1820+4\sqrt{207022}}{8}
$