4/5x-2=2/15x

Solution for 4/5x-2=2/15x equation:

4/5x-2=2/15x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 15x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


60x/75x^2+(-10x)/75x^2-2=0

We multiply all the terms by the denominator


60x+(-10x)-2*75x^2=0

Wy multiply elements

-150x^2+60x+(-10x)=0

We get rid of parentheses

-150x^2+60x-10x=0

We add all the numbers together, and all the variables

-150x^2+50x=0

a = -150; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·(-150)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*-150}=\frac{-100}{-300}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*-150}=\frac{0}{-300}
=0
$