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

Solution for 2(x+5)=3(-2+1/3x) equation:

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

We move all terms to the left:

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


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

2x-(3(1/3x-2))+10=0

We multiply all the terms by the denominator


2x*3x+10*3x-2))-(3(1-2))=0

We add all the numbers together, and all the variables

2x*3x+10*3x-2))-(3(-1))=0

We add all the numbers together, and all the variables

2x*3x+10*3x=0

Wy multiply elements

6x^2+30x=0

a = 6; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·6·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*6}=\frac{-60}{12}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*6}=\frac{0}{12}
=0
$