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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 15x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


90x^2/1125x^2+750x/1125x^2+(-300x)/1125x^2+2=0

We multiply all the terms by the denominator


90x^2+750x+(-300x)+2*1125x^2=0

Wy multiply elements

90x^2+2250x^2+750x+(-300x)=0

We get rid of parentheses

90x^2+2250x^2+750x-300x=0

We add all the numbers together, and all the variables

2340x^2+450x=0

a = 2340; b = 450; c = 0;
Δ = b2-4ac
Δ = 4502-4·2340·0
Δ = 202500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{202500}=450$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(450)-450}{2*2340}=\frac{-900}{4680}
=-5/26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(450)+450}{2*2340}=\frac{0}{4680}
=0
$