19x=x(x-3)

Solution for 19x=x(x-3) equation:

19x=x(x-3)

We move all terms to the left:

19x-(x(x-3))=0


We calculate terms in parentheses: -(x(x-3)), so:

x(x-3)

We multiply parentheses

x^2-3x

Back to the equation:

-(x^2-3x)


We get rid of parentheses

-x^2+19x+3x=0

We add all the numbers together, and all the variables

-1x^2+22x=0

a = -1; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-1)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-1}=\frac{-44}{-2}
=+22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-1}=\frac{0}{-2}
=0
$