3/2x-10/3x=11/18

Solution for 3/2x-10/3x=11/18 equation:

3/2x-10/3x=11/18

We move all terms to the left:

3/2x-10/3x-(11/18)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-10/3x-(+11/18)=0

We get rid of parentheses

3/2x-10/3x-11/18=0

We calculate fractions


(-198x^2)/108x^2+162x/108x^2+(-360x)/108x^2=0

We multiply all the terms by the denominator


(-198x^2)+162x+(-360x)=0

We get rid of parentheses

-198x^2+162x-360x=0

We add all the numbers together, and all the variables

-198x^2-198x=0

a = -198; b = -198; c = 0;
Δ = b2-4ac
Δ = -1982-4·(-198)·0
Δ = 39204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39204}=198$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-198)-198}{2*-198}=\frac{0}{-396}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-198)+198}{2*-198}=\frac{396}{-396}
=-1
$