3/2x+5=2/3x-10

Solution for 3/2x+5=2/3x-10 equation:

3/2x+5=2/3x-10

We move all terms to the left:

3/2x+5-(2/3x-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-10)!=0

x∈R


We get rid of parentheses

3/2x-2/3x+10+5=0

We calculate fractions


9x/6x^2+(-4x)/6x^2+10+5=0

We add all the numbers together, and all the variables

9x/6x^2+(-4x)/6x^2+15=0

We multiply all the terms by the denominator


9x+(-4x)+15*6x^2=0

Wy multiply elements

90x^2+9x+(-4x)=0

We get rid of parentheses

90x^2+9x-4x=0

We add all the numbers together, and all the variables

90x^2+5x=0

a = 90; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·90·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*90}=\frac{-10}{180}
=-1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*90}=\frac{0}{180}
=0
$