6x-3+5x-2.5=x(2x-1)

Solution for 6x-3+5x-2.5=x(2x-1) equation:

6x-3+5x-2.5=x(2x-1)

We move all terms to the left:

6x-3+5x-2.5-(x(2x-1))=0

We add all the numbers together, and all the variables

11x-(x(2x-1))-5.5=0


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

x(2x-1)

We multiply parentheses

2x^2-1x

Back to the equation:

-(2x^2-1x)


We get rid of parentheses

-2x^2+11x+1x-5.5=0

We add all the numbers together, and all the variables

-2x^2+12x-5.5=0

a = -2; b = 12; c = -5.5;
Δ = b2-4ac
Δ = 122-4·(-2)·(-5.5)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-10}{2*-2}=\frac{-22}{-4}
=5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+10}{2*-2}=\frac{-2}{-4}
=1/2
$