(2n+22)=5/8n

Solution for (2n+22)=5/8n equation:

(2n+22)=5/8n

We move all terms to the left:

(2n+22)-(5/8n)=0


Domain of the equation: 8n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(2n+22)-(+5/8n)=0

We get rid of parentheses

2n-5/8n+22=0

We multiply all the terms by the denominator


2n*8n+22*8n-5=0

Wy multiply elements

16n^2+176n-5=0

a = 16; b = 176; c = -5;
Δ = b2-4ac
Δ = 1762-4·16·(-5)
Δ = 31296
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:

$\sqrt{\Delta}=\sqrt{31296}=\sqrt{64*489}=\sqrt{64}*\sqrt{489}=8\sqrt{489}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(176)-8\sqrt{489}}{2*16}=\frac{-176-8\sqrt{489}}{32}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(176)+8\sqrt{489}}{2*16}=\frac{-176+8\sqrt{489}}{32}
$