1/3n-7=2n-12

Solution for 1/3n-7=2n-12 equation:

1/3n-7=2n-12

We move all terms to the left:

1/3n-7-(2n-12)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We get rid of parentheses

1/3n-2n+12-7=0

We multiply all the terms by the denominator


-2n*3n+12*3n-7*3n+1=0

Wy multiply elements

-6n^2+36n-21n+1=0

We add all the numbers together, and all the variables

-6n^2+15n+1=0

a = -6; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·(-6)·1
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{249}}{2*-6}=\frac{-15-\sqrt{249}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{249}}{2*-6}=\frac{-15+\sqrt{249}}{-12}
$