1/5x=1/4x+5

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Solution for 1/5x=1/4x+5 equation:



1/5x=1/4x+5
We move all terms to the left:
1/5x-(1/4x+5)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 4x+5)!=0
x∈R
We get rid of parentheses
1/5x-1/4x-5=0
We calculate fractions
4x/20x^2+(-5x)/20x^2-5=0
We multiply all the terms by the denominator
4x+(-5x)-5*20x^2=0
Wy multiply elements
-100x^2+4x+(-5x)=0
We get rid of parentheses
-100x^2+4x-5x=0
We add all the numbers together, and all the variables
-100x^2-1x=0
a = -100; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-100)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-100}=\frac{0}{-200} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-100}=\frac{2}{-200} =-1/100 $

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