25-x^2=9x-9

Solution for 25-x^2=9x-9 equation:

25-x^2=9x-9

We move all terms to the left:

25-x^2-(9x-9)=0

We add all the numbers together, and all the variables

-1x^2-(9x-9)+25=0

We get rid of parentheses

-1x^2-9x+9+25=0

We add all the numbers together, and all the variables

-1x^2-9x+34=0

a = -1; b = -9; c = +34;
Δ = b2-4ac
Δ = -92-4·(-1)·34
Δ = 217
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{-(-9)-\sqrt{217}}{2*-1}=\frac{9-\sqrt{217}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{217}}{2*-1}=\frac{9+\sqrt{217}}{-2}
$