3+2/3x=11-2/5x

Solution for 3+2/3x=11-2/5x equation:

3+2/3x=11-2/5x

We move all terms to the left:

3+2/3x-(11-2/5x)=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-(-2/5x+11)+3=0

We get rid of parentheses

2/3x+2/5x-11+3=0

We calculate fractions


10x/15x^2+6x/15x^2-11+3=0

We add all the numbers together, and all the variables

10x/15x^2+6x/15x^2-8=0

We multiply all the terms by the denominator


10x+6x-8*15x^2=0

We add all the numbers together, and all the variables

16x-8*15x^2=0

Wy multiply elements

-120x^2+16x=0

a = -120; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-120)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-120}=\frac{-32}{-240}
=2/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-120}=\frac{0}{-240}
=0
$