20-4x-18/x+2x-7=0

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Solution for 20-4x-18/x+2x-7=0 equation:



20-4x-18/x+2x-7=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
-2x-18/x+13=0
We multiply all the terms by the denominator
-2x*x+13*x-18=0
We add all the numbers together, and all the variables
13x-2x*x-18=0
Wy multiply elements
-2x^2+13x-18=0
a = -2; b = 13; c = -18;
Δ = b2-4ac
Δ = 132-4·(-2)·(-18)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-5}{2*-2}=\frac{-18}{-4} =4+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5}{2*-2}=\frac{-8}{-4} =+2 $

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