2/5x-2=11-1/4x

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Solution for 2/5x-2=11-1/4x equation:



2/5x-2=11-1/4x
We move all terms to the left:
2/5x-2-(11-1/4x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 4x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
2/5x-(-1/4x+11)-2=0
We get rid of parentheses
2/5x+1/4x-11-2=0
We calculate fractions
8x/20x^2+5x/20x^2-11-2=0
We add all the numbers together, and all the variables
8x/20x^2+5x/20x^2-13=0
We multiply all the terms by the denominator
8x+5x-13*20x^2=0
We add all the numbers together, and all the variables
13x-13*20x^2=0
Wy multiply elements
-260x^2+13x=0
a = -260; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-260)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-260}=\frac{-26}{-520} =1/20 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-260}=\frac{0}{-520} =0 $

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