1/2x+1/3x=7/9

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Solution for 1/2x+1/3x=7/9 equation:



1/2x+1/3x=7/9
We move all terms to the left:
1/2x+1/3x-(7/9)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
1/2x+1/3x-(+7/9)=0
We get rid of parentheses
1/2x+1/3x-7/9=0
We calculate fractions
(-126x^2)/486x^2+243x/486x^2+162x/486x^2=0
We multiply all the terms by the denominator
(-126x^2)+243x+162x=0
We add all the numbers together, and all the variables
(-126x^2)+405x=0
We get rid of parentheses
-126x^2+405x=0
a = -126; b = 405; c = 0;
Δ = b2-4ac
Δ = 4052-4·(-126)·0
Δ = 164025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{164025}=405$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(405)-405}{2*-126}=\frac{-810}{-252} =3+3/14 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(405)+405}{2*-126}=\frac{0}{-252} =0 $

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