6/2n-5=2n-7

Solution for 6/2n-5=2n-7 equation:

6/2n-5=2n-7

We move all terms to the left:

6/2n-5-(2n-7)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

6/2n-2n+7-5=0

We multiply all the terms by the denominator


-2n*2n+7*2n-5*2n+6=0

Wy multiply elements

-4n^2+14n-10n+6=0

We add all the numbers together, and all the variables

-4n^2+4n+6=0

a = -4; b = 4; c = +6;
Δ = b2-4ac
Δ = 42-4·(-4)·6
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{7}}{2*-4}=\frac{-4-4\sqrt{7}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{7}}{2*-4}=\frac{-4+4\sqrt{7}}{-8}
$