(/34n-28)=2n

Solution for (/34n-28)=2n equation:

(/34n-28)=2n

We move all terms to the left:

(/34n-28)-(2n)=0


Domain of the equation: 34n-28)!=0

n∈R


We add all the numbers together, and all the variables

-2n+(/34n-28)=0

We get rid of parentheses

-2n+/34n-28=0

We multiply all the terms by the denominator


-2n*34n-28*34n+=0

We add all the numbers together, and all the variables

-2n*34n-28*34n=0

Wy multiply elements

-68n^2-952n=0

a = -68; b = -952; c = 0;
Δ = b2-4ac
Δ = -9522-4·(-68)·0
Δ = 906304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{906304}=952$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-952)-952}{2*-68}=\frac{0}{-136}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-952)+952}{2*-68}=\frac{1904}{-136}
=-14
$