23x/33x-23=2x

Solution for 23x/33x-23=2x equation:

23x/33x-23=2x

We move all terms to the left:

23x/33x-23-(2x)=0


Domain of the equation: 33x!=0

x!=0/33

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+23x/33x-23=0

We multiply all the terms by the denominator


-2x*33x+23x-23*33x=0

We add all the numbers together, and all the variables

23x-2x*33x-23*33x=0

Wy multiply elements

-66x^2+23x-759x=0

We add all the numbers together, and all the variables

-66x^2-736x=0

a = -66; b = -736; c = 0;
Δ = b2-4ac
Δ = -7362-4·(-66)·0
Δ = 541696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{541696}=736$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-736)-736}{2*-66}=\frac{0}{-132}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-736)+736}{2*-66}=\frac{1472}{-132}
=-11+5/33
$