x+7-(5/x-2)=5

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Solution for x+7-(5/x-2)=5 equation:



x+7-(5/x-2)=5
We move all terms to the left:
x+7-(5/x-2)-(5)=0
Domain of the equation: x-2)!=0
x∈R
We add all the numbers together, and all the variables
x-(5/x-2)+2=0
We get rid of parentheses
x-5/x+2+2=0
We multiply all the terms by the denominator
x*x+2*x+2*x-5=0
We add all the numbers together, and all the variables
4x+x*x-5=0
Wy multiply elements
x^2+4x-5=0
a = 1; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·1·(-5)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6}{2*1}=\frac{-10}{2} =-5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6}{2*1}=\frac{2}{2} =1 $

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