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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-12x)/15x^2+(-10x)/15x^2+3+4=0

We add all the numbers together, and all the variables

(-12x)/15x^2+(-10x)/15x^2+7=0

We multiply all the terms by the denominator


(-12x)+(-10x)+7*15x^2=0

Wy multiply elements

105x^2+(-12x)+(-10x)=0

We get rid of parentheses

105x^2-12x-10x=0

We add all the numbers together, and all the variables

105x^2-22x=0

a = 105; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·105·0
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*105}=\frac{0}{210}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*105}=\frac{44}{210}
=22/105
$