3/8n-1/3=5/6*

Solution for 3/8n-1/3=5/6* equation:

3/8n-1/3=5/6*

We move all terms to the left:

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


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/8n-1/3-5/6*=0

We calculate fractions


(-288n^2)/864n^2+()/864n^2+(-360n)/864n^2=0

We multiply all the terms by the denominator


(-288n^2)+(-360n)+()=0

We add all the numbers together, and all the variables

(-288n^2)+(-360n)=0

We get rid of parentheses

-288n^2-360n=0

a = -288; b = -360; c = 0;
Δ = b2-4ac
Δ = -3602-4·(-288)·0
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-360}{2*-288}=\frac{0}{-576}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+360}{2*-288}=\frac{720}{-576}
=-1+1/4
$