1/298n+6)=4n+3

Solution for 1/298n+6)=4n+3 equation:

1/298n+6)=4n+3

We move all terms to the left:

1/298n+6)-(4n+3)=0


Domain of the equation: 298n!=0

n!=0/298

n!=0

n∈R


We add all the numbers together, and all the variables

1/298n+6)-(4n=0

We multiply all the terms by the denominator


-4n*298n+1+6=0

We add all the numbers together, and all the variables

-4n*298n+7=0

Wy multiply elements

-1192n^2+7=0

a = -1192; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-1192)·7
Δ = 33376
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:

$\sqrt{\Delta}=\sqrt{33376}=\sqrt{16*2086}=\sqrt{16}*\sqrt{2086}=4\sqrt{2086}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2086}}{2*-1192}=\frac{0-4\sqrt{2086}}{-2384}
=-\frac{4\sqrt{2086}}{-2384}
=-\frac{\sqrt{2086}}{-596}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2086}}{2*-1192}=\frac{0+4\sqrt{2086}}{-2384}
=\frac{4\sqrt{2086}}{-2384}
=\frac{\sqrt{2086}}{-596}
$