1/2x+3=2/3x-7

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Solution for 1/2x+3=2/3x-7 equation:



1/2x+3=2/3x-7
We move all terms to the left:
1/2x+3-(2/3x-7)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x-7)!=0
x∈R
We get rid of parentheses
1/2x-2/3x+7+3=0
We calculate fractions
3x/6x^2+(-4x)/6x^2+7+3=0
We add all the numbers together, and all the variables
3x/6x^2+(-4x)/6x^2+10=0
We multiply all the terms by the denominator
3x+(-4x)+10*6x^2=0
Wy multiply elements
60x^2+3x+(-4x)=0
We get rid of parentheses
60x^2+3x-4x=0
We add all the numbers together, and all the variables
60x^2-1x=0
a = 60; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·60·0
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*60}=\frac{0}{120} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*60}=\frac{2}{120} =1/60 $

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