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

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

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

We move all terms to the left:

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


Domain of the equation: 35x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+2/35x)+2=0

We get rid of parentheses

3x-2/35x+2=0

We multiply all the terms by the denominator


3x*35x+2*35x-2=0

Wy multiply elements

105x^2+70x-2=0

a = 105; b = 70; c = -2;
Δ = b2-4ac
Δ = 702-4·105·(-2)
Δ = 5740
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5740}=\sqrt{4*1435}=\sqrt{4}*\sqrt{1435}=2\sqrt{1435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{1435}}{2*105}=\frac{-70-2\sqrt{1435}}{210}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{1435}}{2*105}=\frac{-70+2\sqrt{1435}}{210}
$