8/n-(4n+7)=13

Solution for 8/n-(4n+7)=13 equation:

8/n-(4n+7)=13

We move all terms to the left:

8/n-(4n+7)-(13)=0


Domain of the equation: n!=0

n∈R


We get rid of parentheses

8/n-4n-7-13=0

We multiply all the terms by the denominator


-4n*n-7*n-13*n+8=0

We add all the numbers together, and all the variables

-20n-4n*n+8=0

Wy multiply elements

-4n^2-20n+8=0

a = -4; b = -20; c = +8;
Δ = b2-4ac
Δ = -202-4·(-4)·8
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{33}}{2*-4}=\frac{20-4\sqrt{33}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{33}}{2*-4}=\frac{20+4\sqrt{33}}{-8}
$