1/6n+7=-2n+20

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Solution for 1/6n+7=-2n+20 equation:



1/6n+7=-2n+20
We move all terms to the left:
1/6n+7-(-2n+20)=0
Domain of the equation: 6n!=0
n!=0/6
n!=0
n∈R
We get rid of parentheses
1/6n+2n-20+7=0
We multiply all the terms by the denominator
2n*6n-20*6n+7*6n+1=0
Wy multiply elements
12n^2-120n+42n+1=0
We add all the numbers together, and all the variables
12n^2-78n+1=0
a = 12; b = -78; c = +1;
Δ = b2-4ac
Δ = -782-4·12·1
Δ = 6036
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:
$\sqrt{\Delta}=\sqrt{6036}=\sqrt{4*1509}=\sqrt{4}*\sqrt{1509}=2\sqrt{1509}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1509}}{2*12}=\frac{78-2\sqrt{1509}}{24} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1509}}{2*12}=\frac{78+2\sqrt{1509}}{24} $

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