19-3n+25/nn=5

Solution for 19-3n+25/nn=5 equation:

19-3n+25/nn=5

We move all terms to the left:

19-3n+25/nn-(5)=0


Domain of the equation: nn!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-3n+25/nn+14=0

We multiply all the terms by the denominator


-3n*nn+14*nn+25=0

Wy multiply elements

-3n^2+14n+25=0

a = -3; b = 14; c = +25;
Δ = b2-4ac
Δ = 142-4·(-3)·25
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{31}}{2*-3}=\frac{-14-4\sqrt{31}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{31}}{2*-3}=\frac{-14+4\sqrt{31}}{-6}
$