2n-3/5n=5

Solution for 2n-3/5n=5 equation:

2n-3/5n=5

We move all terms to the left:

2n-3/5n-(5)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We multiply all the terms by the denominator


2n*5n-5*5n-3=0

Wy multiply elements

10n^2-25n-3=0

a = 10; b = -25; c = -3;
Δ = b2-4ac
Δ = -252-4·10·(-3)
Δ = 745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{745}}{2*10}=\frac{25-\sqrt{745}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{745}}{2*10}=\frac{25+\sqrt{745}}{20}
$