3/8n+5(n-6)=1+7/8n-2

Solution for 3/8n+5(n-6)=1+7/8n-2 equation:

3/8n+5(n-6)=1+7/8n-2

We move all terms to the left:

3/8n+5(n-6)-(1+7/8n-2)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R



Domain of the equation: 8n-2)!=0

n∈R


We add all the numbers together, and all the variables

3/8n+5(n-6)-(7/8n-1)=0

We multiply parentheses

3/8n+5n-(7/8n-1)-30=0

We get rid of parentheses

3/8n+5n-7/8n+1-30=0

We multiply all the terms by the denominator


5n*8n+1*8n-30*8n+3-7=0

We add all the numbers together, and all the variables

5n*8n+1*8n-30*8n-4=0

Wy multiply elements

40n^2+8n-240n-4=0

We add all the numbers together, and all the variables

40n^2-232n-4=0

a = 40; b = -232; c = -4;
Δ = b2-4ac
Δ = -2322-4·40·(-4)
Δ = 54464
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:

$\sqrt{\Delta}=\sqrt{54464}=\sqrt{64*851}=\sqrt{64}*\sqrt{851}=8\sqrt{851}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-232)-8\sqrt{851}}{2*40}=\frac{232-8\sqrt{851}}{80}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-232)+8\sqrt{851}}{2*40}=\frac{232+8\sqrt{851}}{80}
$