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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-10x)/15x^2+(-12x)/15x^2+3=0

We multiply all the terms by the denominator


(-10x)+(-12x)+3*15x^2=0

Wy multiply elements

45x^2+(-10x)+(-12x)=0

We get rid of parentheses

45x^2-10x-12x=0

We add all the numbers together, and all the variables

45x^2-22x=0

a = 45; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·45·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*45}=\frac{0}{90}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*45}=\frac{44}{90}
=22/45
$