1/5x+8=17-1/20x.

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Solution for 1/5x+8=17-1/20x. equation:



1/5x+8=17-1/20x.
We move all terms to the left:
1/5x+8-(17-1/20x.)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 20x.)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/5x-(-1/20x.+17)+8=0
We get rid of parentheses
1/5x+1/20x.-17+8=0
We calculate fractions
20x/100x^2+5x/100x^2-17+8=0
We add all the numbers together, and all the variables
20x/100x^2+5x/100x^2-9=0
We multiply all the terms by the denominator
20x+5x-9*100x^2=0
We add all the numbers together, and all the variables
25x-9*100x^2=0
Wy multiply elements
-900x^2+25x=0
a = -900; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-900)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-900}=\frac{-50}{-1800} =1/36 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-900}=\frac{0}{-1800} =0 $

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