(19+x)x=x+9

Solution for (19+x)x=x+9 equation:

(19+x)x=x+9

We move all terms to the left:

(19+x)x-(x+9)=0

We add all the numbers together, and all the variables

(x+19)x-(x+9)=0

We multiply parentheses

x^2+19x-(x+9)=0

We get rid of parentheses

x^2+19x-x-9=0

We add all the numbers together, and all the variables

x^2+18x-9=0

a = 1; b = 18; c = -9;
Δ = b2-4ac
Δ = 182-4·1·(-9)
Δ = 360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{10}}{2*1}=\frac{-18-6\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{10}}{2*1}=\frac{-18+6\sqrt{10}}{2}
$