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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


15x/10x^2+(-4x)/10x^2-9+3=0

We add all the numbers together, and all the variables

15x/10x^2+(-4x)/10x^2-6=0

We multiply all the terms by the denominator


15x+(-4x)-6*10x^2=0

Wy multiply elements

-60x^2+15x+(-4x)=0

We get rid of parentheses

-60x^2+15x-4x=0

We add all the numbers together, and all the variables

-60x^2+11x=0

a = -60; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-60)·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*-60}=\frac{-22}{-120}
=11/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-60}=\frac{0}{-120}
=0
$