3.8n-13=1/4n+5

Solution for 3.8n-13=1/4n+5 equation:

3.8n-13=1/4n+5

We move all terms to the left:

3.8n-13-(1/4n+5)=0


Domain of the equation: 4n+5)!=0

n∈R


We get rid of parentheses

3.8n-1/4n-5-13=0

We multiply all the terms by the denominator


(3.8n)*4n-5*4n-13*4n-1=0

We add all the numbers together, and all the variables

(+3.8n)*4n-5*4n-13*4n-1=0

We multiply parentheses

12n^2-5*4n-13*4n-1=0

Wy multiply elements

12n^2-20n-52n-1=0

We add all the numbers together, and all the variables

12n^2-72n-1=0

a = 12; b = -72; c = -1;
Δ = b2-4ac
Δ = -722-4·12·(-1)
Δ = 5232
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:

$\sqrt{\Delta}=\sqrt{5232}=\sqrt{16*327}=\sqrt{16}*\sqrt{327}=4\sqrt{327}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{327}}{2*12}=\frac{72-4\sqrt{327}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{327}}{2*12}=\frac{72+4\sqrt{327}}{24}
$