20/100*x-108=x

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Solution for 20/100*x-108=x equation:



20/100x-108=x
We move all terms to the left:
20/100x-108-(x)=0
Domain of the equation: 100x!=0
x!=0/100
x!=0
x∈R
We add all the numbers together, and all the variables
-1x+20/100x-108=0
We multiply all the terms by the denominator
-1x*100x-108*100x+20=0
Wy multiply elements
-100x^2-10800x+20=0
a = -100; b = -10800; c = +20;
Δ = b2-4ac
Δ = -108002-4·(-100)·20
Δ = 116648000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{116648000}=\sqrt{1600*72905}=\sqrt{1600}*\sqrt{72905}=40\sqrt{72905}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10800)-40\sqrt{72905}}{2*-100}=\frac{10800-40\sqrt{72905}}{-200} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10800)+40\sqrt{72905}}{2*-100}=\frac{10800+40\sqrt{72905}}{-200} $

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