4/5x+3/4=5/2x-1

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Solution for 4/5x+3/4=5/2x-1 equation:



4/5x+3/4=5/2x-1
We move all terms to the left:
4/5x+3/4-(5/2x-1)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 2x-1)!=0
x∈R
We get rid of parentheses
4/5x-5/2x+1+3/4=0
We calculate fractions
60x^2/160x^2+128x/160x^2+(-400x)/160x^2+1=0
We multiply all the terms by the denominator
60x^2+128x+(-400x)+1*160x^2=0
Wy multiply elements
60x^2+160x^2+128x+(-400x)=0
We get rid of parentheses
60x^2+160x^2+128x-400x=0
We add all the numbers together, and all the variables
220x^2-272x=0
a = 220; b = -272; c = 0;
Δ = b2-4ac
Δ = -2722-4·220·0
Δ = 73984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{73984}=272$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-272)-272}{2*220}=\frac{0}{440} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-272)+272}{2*220}=\frac{544}{440} =1+13/55 $

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