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: 3*5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


3x*3*5x+2*3*5x-2=0

Wy multiply elements

45x^2*5+30x*5-2=0

Wy multiply elements

225x^2+150x-2=0

a = 225; b = 150; c = -2;
Δ = b2-4ac
Δ = 1502-4·225·(-2)
Δ = 24300
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:

$\sqrt{\Delta}=\sqrt{24300}=\sqrt{8100*3}=\sqrt{8100}*\sqrt{3}=90\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-90\sqrt{3}}{2*225}=\frac{-150-90\sqrt{3}}{450}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+90\sqrt{3}}{2*225}=\frac{-150+90\sqrt{3}}{450}
$