-3/5x+1-1/3x=61/33

Solution for -3/5x+1-1/3x=61/33 equation:

-3/5x+1-1/3x=61/33

We move all terms to the left:

-3/5x+1-1/3x-(61/33)=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


We add all the numbers together, and all the variables

-3/5x-1/3x+1-(+61/33)=0

We get rid of parentheses

-3/5x-1/3x+1-61/33=0

We calculate fractions


(-2745x^2)/1485x^2+(-891x)/1485x^2+(-495x)/1485x^2+1=0

We multiply all the terms by the denominator


(-2745x^2)+(-891x)+(-495x)+1*1485x^2=0

Wy multiply elements

(-2745x^2)+1485x^2+(-891x)+(-495x)=0

We get rid of parentheses

-2745x^2+1485x^2-891x-495x=0

We add all the numbers together, and all the variables

-1260x^2-1386x=0

a = -1260; b = -1386; c = 0;
Δ = b2-4ac
Δ = -13862-4·(-1260)·0
Δ = 1920996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1920996}=1386$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1386)-1386}{2*-1260}=\frac{0}{-2520}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1386)+1386}{2*-1260}=\frac{2772}{-2520}
=-1+1/10
$