2.5x-4.5=5/3x-3

Solution for 2.5x-4.5=5/3x-3 equation:

2.5x-4.5=5/3x-3

We move all terms to the left:

2.5x-4.5-(5/3x-3)=0


Domain of the equation: 3x-3)!=0

x∈R


We get rid of parentheses

2.5x-5/3x+3-4.5=0

We multiply all the terms by the denominator


(2.5x)*3x+3*3x-(4.5)*3x-5=0

We add all the numbers together, and all the variables

(+2.5x)*3x+3*3x-(4.5)*3x-5=0

We multiply parentheses

6x^2+3*3x-13.5x-5=0

Wy multiply elements

6x^2+9x-13.5x-5=0

We add all the numbers together, and all the variables

6x^2-4.5x-5=0

a = 6; b = -4.5; c = -5;
Δ = b2-4ac
Δ = -4.52-4·6·(-5)
Δ = 140.25
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{-(-4.5)-\sqrt{140.25}}{2*6}=\frac{4.5-\sqrt{140.25}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.5)+\sqrt{140.25}}{2*6}=\frac{4.5+\sqrt{140.25}}{12}
$