9=8x-0.83x^2

Solution for 9=8x-0.83x^2 equation:

9=8x-0.83x^2

We move all terms to the left:

9-(8x-0.83x^2)=0

We get rid of parentheses

0.83x^2-8x+9=0

a = 0.83; b = -8; c = +9;
Δ = b2-4ac
Δ = -82-4·0.83·9
Δ = 34.12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-\sqrt{34.12}}{2*0.83}=\frac{8-\sqrt{34.12}}{1.66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+\sqrt{34.12}}{2*0.83}=\frac{8+\sqrt{34.12}}{1.66}
$