2/3x=0.5x+5

Solution for 2/3x=0.5x+5 equation:

2/3x=0.5x+5

We move all terms to the left:

2/3x-(0.5x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-0.5x-5=0

We multiply all the terms by the denominator


-(0.5x)*3x-5*3x+2=0

We add all the numbers together, and all the variables

-(+0.5x)*3x-5*3x+2=0

We multiply parentheses

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

Wy multiply elements

-0x^2-15x+2=0

We add all the numbers together, and all the variables

-1x^2-15x+2=0

a = -1; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·(-1)·2
Δ = 233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{233}}{2*-1}=\frac{15-\sqrt{233}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{233}}{2*-1}=\frac{15+\sqrt{233}}{-2}
$