3/2x+3=1/5x+9

Solution for 3/2x+3=1/5x+9 equation:

3/2x+3=1/5x+9

We move all terms to the left:

3/2x+3-(1/5x+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-1/5x-9+3=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-60x^2+13x=0

a = -60; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-60)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-60}=\frac{-26}{-120}
=13/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-60}=\frac{0}{-120}
=0
$