X+5/x=7

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Solution for X+5/x=7 equation:



X+5/X=7
We move all terms to the left:
X+5/X-(7)=0
Domain of the equation: X!=0
X∈R
We multiply all the terms by the denominator
X*X-7*X+5=0
We add all the numbers together, and all the variables
-7X+X*X+5=0
Wy multiply elements
X^2-7X+5=0
a = 1; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·1·5
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{29}}{2*1}=\frac{7-\sqrt{29}}{2} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{29}}{2*1}=\frac{7+\sqrt{29}}{2} $

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