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

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



2/3x-1/2x=-5
We move all terms to the left:
2/3x-1/2x-(-5)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
2/3x-1/2x+5=0
We calculate fractions
4x/6x^2+(-3x)/6x^2+5=0
We multiply all the terms by the denominator
4x+(-3x)+5*6x^2=0
Wy multiply elements
30x^2+4x+(-3x)=0
We get rid of parentheses
30x^2+4x-3x=0
We add all the numbers together, and all the variables
30x^2+x=0
a = 30; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·30·0
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*30}=\frac{-2}{60} =-1/30 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*30}=\frac{0}{60} =0 $

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