1/3x+2x=3x-2.5

Solution for 1/3x+2x=3x-2.5 equation:

1/3x+2x=3x-2.5

We move all terms to the left:

1/3x+2x-(3x-2.5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/3x-(3x-2.5)=0

We get rid of parentheses

2x+1/3x-3x+2.5=0

We multiply all the terms by the denominator


2x*3x-3x*3x+(2.5)*3x+1=0

We multiply parentheses

2x*3x-3x*3x+7.5x+1=0

Wy multiply elements

6x^2-9x^2+7.5x+1=0

We add all the numbers together, and all the variables

-3x^2+7.5x+1=0

a = -3; b = 7.5; c = +1;
Δ = b2-4ac
Δ = 7.52-4·(-3)·1
Δ = 68.25
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{-(7.5)-\sqrt{68.25}}{2*-3}=\frac{-7.5-\sqrt{68.25}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7.5)+\sqrt{68.25}}{2*-3}=\frac{-7.5+\sqrt{68.25}}{-6}
$