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

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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} $

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