9x=x^2-8x+16

Solution for 9x=x^2-8x+16 equation:

9x=x^2-8x+16

We move all terms to the left:

9x-(x^2-8x+16)=0

We get rid of parentheses

-x^2+9x+8x-16=0

We add all the numbers together, and all the variables

-1x^2+17x-16=0

a = -1; b = 17; c = -16;
Δ = b2-4ac
Δ = 172-4·(-1)·(-16)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-15}{2*-1}=\frac{-32}{-2}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+15}{2*-1}=\frac{-2}{-2}
=1
$