19x=13x(x+1)

Solution for 19x=13x(x+1) equation:

19x=13x(x+1)

We move all terms to the left:

19x-(13x(x+1))=0


We calculate terms in parentheses: -(13x(x+1)), so:

13x(x+1)

We multiply parentheses

13x^2+13x

Back to the equation:

-(13x^2+13x)


We get rid of parentheses

-13x^2+19x-13x=0

We add all the numbers together, and all the variables

-13x^2+6x=0

a = -13; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-13)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-13}=\frac{-12}{-26}
=6/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-13}=\frac{0}{-26}
=0
$