2+2/3x=1-5/4x

Solution for 2+2/3x=1-5/4x equation:

2+2/3x=1-5/4x

We move all terms to the left:

2+2/3x-(1-5/4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-5/4x+1)+2=0

We get rid of parentheses

2/3x+5/4x-1+2=0

We calculate fractions


8x/12x^2+15x/12x^2-1+2=0

We add all the numbers together, and all the variables

8x/12x^2+15x/12x^2+1=0

We multiply all the terms by the denominator


8x+15x+1*12x^2=0

We add all the numbers together, and all the variables

23x+1*12x^2=0

Wy multiply elements

12x^2+23x=0

a = 12; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·12·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*12}=\frac{-46}{24}
=-1+11/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*12}=\frac{0}{24}
=0
$