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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

5x+2x-(x(2x-1))-6=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 add all the numbers together, and all the variables

7x-(2x^2-1x)-6=0

We get rid of parentheses

-2x^2+7x+1x-6=0

We add all the numbers together, and all the variables

-2x^2+8x-6=0

a = -2; b = 8; c = -6;
Δ = b2-4ac
Δ = 82-4·(-2)·(-6)
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{-(8)-4}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4}{2*-2}=\frac{-4}{-4}
=1
$