2/3x+3=4/5x+9

Solution for 2/3x+3=4/5x+9 equation:

2/3x+3=4/5x+9

We move all terms to the left:

2/3x+3-(4/5x+9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+9)!=0

x∈R


We get rid of parentheses

2/3x-4/5x-9+3=0

We calculate fractions


10x/15x^2+(-12x)/15x^2-9+3=0

We add all the numbers together, and all the variables

10x/15x^2+(-12x)/15x^2-6=0

We multiply all the terms by the denominator


10x+(-12x)-6*15x^2=0

Wy multiply elements

-90x^2+10x+(-12x)=0

We get rid of parentheses

-90x^2+10x-12x=0

We add all the numbers together, and all the variables

-90x^2-2x=0

a = -90; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-90)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-90}=\frac{0}{-180}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-90}=\frac{4}{-180}
=-1/45
$