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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

8.5x-(x(2x-1))-3=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+8.5x+1x-3=0

We add all the numbers together, and all the variables

-2x^2+9.5x-3=0

a = -2; b = 9.5; c = -3;
Δ = b2-4ac
Δ = 9.52-4·(-2)·(-3)
Δ = 66.25
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{-(9.5)-\sqrt{66.25}}{2*-2}=\frac{-9.5-\sqrt{66.25}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9.5)+\sqrt{66.25}}{2*-2}=\frac{-9.5+\sqrt{66.25}}{-4}
$