n=12/5n-28

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}
$