3/2x+12/5x=13/20

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Solution for 3/2x+12/5x=13/20 equation:



3/2x+12/5x=13/20
We move all terms to the left:
3/2x+12/5x-(13/20)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
We add all the numbers together, and all the variables
3/2x+12/5x-(+13/20)=0
We get rid of parentheses
3/2x+12/5x-13/20=0
We calculate fractions
(-650x^2)/400x^2+600x/400x^2+960x/400x^2=0
We multiply all the terms by the denominator
(-650x^2)+600x+960x=0
We add all the numbers together, and all the variables
(-650x^2)+1560x=0
We get rid of parentheses
-650x^2+1560x=0
a = -650; b = 1560; c = 0;
Δ = b2-4ac
Δ = 15602-4·(-650)·0
Δ = 2433600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2433600}=1560$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1560)-1560}{2*-650}=\frac{-3120}{-1300} =2+2/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1560)+1560}{2*-650}=\frac{0}{-1300} =0 $

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