2x/3x+3=x/45

Solution for 2x/3x+3=x/45 equation:

2x/3x+3=x/45

We move all terms to the left:

2x/3x+3-(x/45)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x/3x-(+x/45)+3=0

We get rid of parentheses

2x/3x-x/45+3=0

We calculate fractions


(-3x^2)/135x+90x/135x+3=0

We multiply all the terms by the denominator


(-3x^2)+90x+3*135x=0

Wy multiply elements

(-3x^2)+90x+405x=0

We get rid of parentheses

-3x^2+90x+405x=0

We add all the numbers together, and all the variables

-3x^2+495x=0

a = -3; b = 495; c = 0;
Δ = b2-4ac
Δ = 4952-4·(-3)·0
Δ = 245025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{245025}=495$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(495)-495}{2*-3}=\frac{-990}{-6}
=+165
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(495)+495}{2*-3}=\frac{0}{-6}
=0
$