1/2n+45=172n=

Solution for 1/2n+45=172n= equation:

1/2n+45=172n=

We move all terms to the left:

1/2n+45-(172n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

-172n+1/2n+45=0

We multiply all the terms by the denominator


-172n*2n+45*2n+1=0

Wy multiply elements

-344n^2+90n+1=0

a = -344; b = 90; c = +1;
Δ = b2-4ac
Δ = 902-4·(-344)·1
Δ = 9476
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:

$\sqrt{\Delta}=\sqrt{9476}=\sqrt{4*2369}=\sqrt{4}*\sqrt{2369}=2\sqrt{2369}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2369}}{2*-344}=\frac{-90-2\sqrt{2369}}{-688}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2369}}{2*-344}=\frac{-90+2\sqrt{2369}}{-688}
$