-2n+13/6n=6

Solution for -2n+13/6n=6 equation:

-2n+13/6n=6

We move all terms to the left:

-2n+13/6n-(6)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We multiply all the terms by the denominator


-2n*6n-6*6n+13=0

Wy multiply elements

-12n^2-36n+13=0

a = -12; b = -36; c = +13;
Δ = b2-4ac
Δ = -362-4·(-12)·13
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{30}}{2*-12}=\frac{36-8\sqrt{30}}{-24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{30}}{2*-12}=\frac{36+8\sqrt{30}}{-24}
$