3/2x+12=-6/5x+3

Solution for 3/2x+12=-6/5x+3 equation:

3/2x+12=-6/5x+3

We move all terms to the left:

3/2x+12-(-6/5x+3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+3)!=0

x∈R


We get rid of parentheses

3/2x+6/5x-3+12=0

We calculate fractions


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

We add all the numbers together, and all the variables

15x/10x^2+12x/10x^2+9=0

We multiply all the terms by the denominator


15x+12x+9*10x^2=0

We add all the numbers together, and all the variables

27x+9*10x^2=0

Wy multiply elements

90x^2+27x=0

a = 90; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·90·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*90}=\frac{-54}{180}
=-3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*90}=\frac{0}{180}
=0
$