2n-11/5n=16

Solution for 2n-11/5n=16 equation:

2n-11/5n=16

We move all terms to the left:

2n-11/5n-(16)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We multiply all the terms by the denominator


2n*5n-16*5n-11=0

Wy multiply elements

10n^2-80n-11=0

a = 10; b = -80; c = -11;
Δ = b2-4ac
Δ = -802-4·10·(-11)
Δ = 6840
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:

$\sqrt{\Delta}=\sqrt{6840}=\sqrt{36*190}=\sqrt{36}*\sqrt{190}=6\sqrt{190}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-6\sqrt{190}}{2*10}=\frac{80-6\sqrt{190}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+6\sqrt{190}}{2*10}=\frac{80+6\sqrt{190}}{20}
$