3/5x-1/3=-7-2/3x

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Solution for 3/5x-1/3=-7-2/3x equation:



3/5x-1/3=-7-2/3x
We move all terms to the left:
3/5x-1/3-(-7-2/3x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
3/5x-(-2/3x-7)-1/3=0
We get rid of parentheses
3/5x+2/3x+7-1/3=0
We calculate fractions
81x/135x^2+10x/135x^2+(-5x)/135x^2+7=0
We multiply all the terms by the denominator
81x+10x+(-5x)+7*135x^2=0
We add all the numbers together, and all the variables
91x+(-5x)+7*135x^2=0
Wy multiply elements
945x^2+91x+(-5x)=0
We get rid of parentheses
945x^2+91x-5x=0
We add all the numbers together, and all the variables
945x^2+86x=0
a = 945; b = 86; c = 0;
Δ = b2-4ac
Δ = 862-4·945·0
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-86}{2*945}=\frac{-172}{1890} =-86/945 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+86}{2*945}=\frac{0}{1890} =0 $

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