2/5x+3=2/3x+13

Solution for 2/5x+3=2/3x+13 equation:

2/5x+3=2/3x+13

We move all terms to the left:

2/5x+3-(2/3x+13)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x+13)!=0

x∈R


We get rid of parentheses

2/5x-2/3x-13+3=0

We calculate fractions


6x/15x^2+(-10x)/15x^2-13+3=0

We add all the numbers together, and all the variables

6x/15x^2+(-10x)/15x^2-10=0

We multiply all the terms by the denominator


6x+(-10x)-10*15x^2=0

Wy multiply elements

-150x^2+6x+(-10x)=0

We get rid of parentheses

-150x^2+6x-10x=0

We add all the numbers together, and all the variables

-150x^2-4x=0

a = -150; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-150)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-150}=\frac{0}{-300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-150}=\frac{8}{-300}
=-2/75
$