20-1/2x=5/8x+2

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Solution for 20-1/2x=5/8x+2 equation:



20-1/2x=5/8x+2
We move all terms to the left:
20-1/2x-(5/8x+2)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 8x+2)!=0
x∈R
We get rid of parentheses
-1/2x-5/8x-2+20=0
We calculate fractions
(-8x)/16x^2+(-10x)/16x^2-2+20=0
We add all the numbers together, and all the variables
(-8x)/16x^2+(-10x)/16x^2+18=0
We multiply all the terms by the denominator
(-8x)+(-10x)+18*16x^2=0
Wy multiply elements
288x^2+(-8x)+(-10x)=0
We get rid of parentheses
288x^2-8x-10x=0
We add all the numbers together, and all the variables
288x^2-18x=0
a = 288; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·288·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*288}=\frac{0}{576} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*288}=\frac{36}{576} =1/16 $

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