2.5*x*(x-3)=(1.5*x-1)*(x-3)

Solution for 2.5*x*(x-3)=(1.5*x-1)*(x-3) equation:

2.5x(x-3)=(1.5x-1)(x-3)

We move all terms to the left:

2.5x(x-3)-((1.5x-1)(x-3))=0

We multiply parentheses

2x^2-6x-((1.5x-1)(x-3))=0

We multiply parentheses ..

2x^2-((+x^2-3x-1x+3))-6x=0


We calculate terms in parentheses: -((+x^2-3x-1x+3)), so:

(+x^2-3x-1x+3)

We get rid of parentheses

x^2-3x-1x+3

We add all the numbers together, and all the variables

x^2-4x+3

Back to the equation:

-(x^2-4x+3)


We add all the numbers together, and all the variables

2x^2-6x-(x^2-4x+3)=0

We get rid of parentheses

2x^2-x^2-6x+4x-3=0

We add all the numbers together, and all the variables

x^2-2x-3=0

a = 1; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·1·(-3)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*1}=\frac{6}{2}
=3
$