-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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

-90x^2+4x-9x=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{0}{-180}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-90}=\frac{10}{-180}
=-1/18
$