-2/5x=1/3x-33

Solution for -2/5x=1/3x-33 equation:

-2/5x=1/3x-33

We move all terms to the left:

-2/5x-(1/3x-33)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-33)!=0

x∈R


We get rid of parentheses

-2/5x-1/3x+33=0

We calculate fractions


(-6x)/15x^2+(-5x)/15x^2+33=0

We multiply all the terms by the denominator


(-6x)+(-5x)+33*15x^2=0

Wy multiply elements

495x^2+(-6x)+(-5x)=0

We get rid of parentheses

495x^2-6x-5x=0

We add all the numbers together, and all the variables

495x^2-11x=0

a = 495; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·495·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*495}=\frac{0}{990}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*495}=\frac{22}{990}
=1/45
$