4n-2/2n=7

Solution for 4n-2/2n=7 equation:

4n-2/2n=7

We move all terms to the left:

4n-2/2n-(7)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We multiply all the terms by the denominator


4n*2n-7*2n-2=0

Wy multiply elements

8n^2-14n-2=0

a = 8; b = -14; c = -2;
Δ = b2-4ac
Δ = -142-4·8·(-2)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{65}}{2*8}=\frac{14-2\sqrt{65}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{65}}{2*8}=\frac{14+2\sqrt{65}}{16}
$