1-2/3x=23-1/15x

Solution for 1-2/3x=23-1/15x equation:

1-2/3x=23-1/15x

We move all terms to the left:

1-2/3x-(23-1/15x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 15x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-2/3x-(-1/15x+23)+1=0

We get rid of parentheses

-2/3x+1/15x-23+1=0

We calculate fractions


(-30x)/45x^2+3x/45x^2-23+1=0

We add all the numbers together, and all the variables

(-30x)/45x^2+3x/45x^2-22=0

We multiply all the terms by the denominator


(-30x)+3x-22*45x^2=0

We add all the numbers together, and all the variables

3x+(-30x)-22*45x^2=0

Wy multiply elements

-990x^2+3x+(-30x)=0

We get rid of parentheses

-990x^2+3x-30x=0

We add all the numbers together, and all the variables

-990x^2-27x=0

a = -990; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-990)·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*-990}=\frac{0}{-1980}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-990}=\frac{54}{-1980}
=-3/110
$