2.5x-3=8+2/3x

Solution for 2.5x-3=8+2/3x equation:

2.5x-3=8+2/3x

We move all terms to the left:

2.5x-3-(8+2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2.5x-(2/3x+8)-3=0

We get rid of parentheses

2.5x-2/3x-8-3=0

We multiply all the terms by the denominator


(2.5x)*3x-8*3x-3*3x-2=0

We add all the numbers together, and all the variables

(+2.5x)*3x-8*3x-3*3x-2=0

We multiply parentheses

6x^2-8*3x-3*3x-2=0

Wy multiply elements

6x^2-24x-9x-2=0

We add all the numbers together, and all the variables

6x^2-33x-2=0

a = 6; b = -33; c = -2;
Δ = b2-4ac
Δ = -332-4·6·(-2)
Δ = 1137
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{-(-33)-\sqrt{1137}}{2*6}=\frac{33-\sqrt{1137}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1137}}{2*6}=\frac{33+\sqrt{1137}}{12}
$