4/5+2/15x=2/3x+4

Solution for 4/5+2/15x=2/3x+4 equation:

4/5+2/15x=2/3x+4

We move all terms to the left:

4/5+2/15x-(2/3x+4)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R



Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

2/15x-2/3x-4+4/5=0

We calculate fractions


540x^2/1125x^2+150x/1125x^2+(-750x)/1125x^2-4=0

We multiply all the terms by the denominator


540x^2+150x+(-750x)-4*1125x^2=0

Wy multiply elements

540x^2-4500x^2+150x+(-750x)=0

We get rid of parentheses

540x^2-4500x^2+150x-750x=0

We add all the numbers together, and all the variables

-3960x^2-600x=0

a = -3960; b = -600; c = 0;
Δ = b2-4ac
Δ = -6002-4·(-3960)·0
Δ = 360000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{360000}=600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-600}{2*-3960}=\frac{0}{-7920}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+600}{2*-3960}=\frac{1200}{-7920}
=-5/33
$