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

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

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

We move all terms to the left:

3/5x-2/3+7/3x+1/5-(2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


determiningTheFunctionDomain
3/5x+7/3x-2-2/3+1/5=0

We calculate fractions


81x/675x^2+875x/675x^2+(-250x)/675x^2+27x/675x^2-2=0

We multiply all the terms by the denominator


81x+875x+(-250x)+27x-2*675x^2=0

We add all the numbers together, and all the variables

983x+(-250x)-2*675x^2=0

Wy multiply elements

-1350x^2+983x+(-250x)=0

We get rid of parentheses

-1350x^2+983x-250x=0

We add all the numbers together, and all the variables

-1350x^2+733x=0

a = -1350; b = 733; c = 0;
Δ = b2-4ac
Δ = 7332-4·(-1350)·0
Δ = 537289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{537289}=733$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(733)-733}{2*-1350}=\frac{-1466}{-2700}
=733/1350
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(733)+733}{2*-1350}=\frac{0}{-2700}
=0
$