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

Solution for (9-x)(x+1)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+8x+9=0

a = -1; b = 8; c = +9;
Δ = b2-4ac
Δ = 82-4·(-1)·9
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*-1}=\frac{2}{-2}
=-1
$