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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


270x^2/540x^2+108x/540x^2+(-160x)/540x^2+160x/540x^2=0

We multiply all the terms by the denominator


270x^2+108x+(-160x)+160x=0

We add all the numbers together, and all the variables

270x^2+268x+(-160x)=0

We get rid of parentheses

270x^2+268x-160x=0

We add all the numbers together, and all the variables

270x^2+108x=0

a = 270; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·270·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*270}=\frac{-216}{540}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*270}=\frac{0}{540}
=0
$