1x(x-1)=9+x

Solution for 1x(x-1)=9+x equation:

1x(x-1)=9+x

We move all terms to the left:

1x(x-1)-(9+x)=0

We add all the numbers together, and all the variables

1x(x-1)-(x+9)=0

We multiply parentheses

x^2-1x-(x+9)=0

We get rid of parentheses

x^2-1x-x-9=0

We add all the numbers together, and all the variables

x^2-2x-9=0

a = 1; b = -2; c = -9;
Δ = b2-4ac
Δ = -22-4·1·(-9)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{10}}{2*1}=\frac{2-2\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{10}}{2*1}=\frac{2+2\sqrt{10}}{2}
$