1/3x-2/3=-9-2/5x

Solution for 1/3x-2/3=-9-2/5x equation:

1/3x-2/3=-9-2/5x

We move all terms to the left:

1/3x-2/3-(-9-2/5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(-2/5x-9)-2/3=0

We get rid of parentheses

1/3x+2/5x+9-2/3=0

We calculate fractions


5x/135x^2+54x/135x^2+(-10x)/135x^2+9=0

We multiply all the terms by the denominator


5x+54x+(-10x)+9*135x^2=0

We add all the numbers together, and all the variables

59x+(-10x)+9*135x^2=0

Wy multiply elements

1215x^2+59x+(-10x)=0

We get rid of parentheses

1215x^2+59x-10x=0

We add all the numbers together, and all the variables

1215x^2+49x=0

a = 1215; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·1215·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*1215}=\frac{-98}{2430}
=-49/1215
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*1215}=\frac{0}{2430}
=0
$