5/6n-3=5/8n+7

Solution for 5/6n-3=5/8n+7 equation:

5/6n-3=5/8n+7

We move all terms to the left:

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


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



Domain of the equation: 8n+7)!=0

n∈R


We get rid of parentheses

5/6n-5/8n-7-3=0

We calculate fractions


40n/48n^2+(-30n)/48n^2-7-3=0

We add all the numbers together, and all the variables

40n/48n^2+(-30n)/48n^2-10=0

We multiply all the terms by the denominator


40n+(-30n)-10*48n^2=0

Wy multiply elements

-480n^2+40n+(-30n)=0

We get rid of parentheses

-480n^2+40n-30n=0

We add all the numbers together, and all the variables

-480n^2+10n=0

a = -480; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-480)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-480}=\frac{-20}{-960}
=1/48
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-480}=\frac{0}{-960}
=0
$