7/2n=3n+4

Solution for 7/2n=3n+4 equation:

7/2n=3n+4

We move all terms to the left:

7/2n-(3n+4)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

7/2n-3n-4=0

We multiply all the terms by the denominator


-3n*2n-4*2n+7=0

Wy multiply elements

-6n^2-8n+7=0

a = -6; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-6)·7
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{58}}{2*-6}=\frac{8-2\sqrt{58}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{58}}{2*-6}=\frac{8+2\sqrt{58}}{-12}
$