5(x-9)-(x+2)(x-9)=0

Solution for 5(x-9)-(x+2)(x-9)=0 equation:

5(x-9)-(x+2)(x-9)=0

We multiply parentheses

5x-(x+2)(x-9)-45=0

We multiply parentheses ..

-(+x^2-9x+2x-18)+5x-45=0

We get rid of parentheses

-x^2+9x-2x+5x+18-45=0

We add all the numbers together, and all the variables

-1x^2+12x-27=0

a = -1; b = 12; c = -27;
Δ = b2-4ac
Δ = 122-4·(-1)·(-27)
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{-(12)-6}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6}{2*-1}=\frac{-6}{-2}
=+3
$