n=12/5n-28

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Solution for n=12/5n-28 equation:



n=12/5n-28
We move all terms to the left:
n-(12/5n-28)=0
Domain of the equation: 5n-28)!=0
n∈R
We get rid of parentheses
n-12/5n+28=0
We multiply all the terms by the denominator
n*5n+28*5n-12=0
Wy multiply elements
5n^2+140n-12=0
a = 5; b = 140; c = -12;
Δ = b2-4ac
Δ = 1402-4·5·(-12)
Δ = 19840
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:
$\sqrt{\Delta}=\sqrt{19840}=\sqrt{64*310}=\sqrt{64}*\sqrt{310}=8\sqrt{310}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-8\sqrt{310}}{2*5}=\frac{-140-8\sqrt{310}}{10} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+8\sqrt{310}}{2*5}=\frac{-140+8\sqrt{310}}{10} $

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