x(-x+8)=9

Solution for x(-x+8)=9 equation:

x(-x+8)=9

We move all terms to the left:

x(-x+8)-(9)=0

We add all the numbers together, and all the variables

x(-1x+8)-9=0

We multiply parentheses

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

a = -1; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·(-1)·(-9)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{7}}{2*-1}=\frac{-8-2\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{7}}{2*-1}=\frac{-8+2\sqrt{7}}{-2}
$