n=7/6n-4

Solution for n=7/6n-4 equation:

n=7/6n-4

We move all terms to the left:

n-(7/6n-4)=0


Domain of the equation: 6n-4)!=0

n∈R


We get rid of parentheses

n-7/6n+4=0

We multiply all the terms by the denominator


n*6n+4*6n-7=0

Wy multiply elements

6n^2+24n-7=0

a = 6; b = 24; c = -7;
Δ = b2-4ac
Δ = 242-4·6·(-7)
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{186}}{2*6}=\frac{-24-2\sqrt{186}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{186}}{2*6}=\frac{-24+2\sqrt{186}}{12}
$