45-x^2=9x-4

Solution for 45-x^2=9x-4 equation:

45-x^2=9x-4

We move all terms to the left:

45-x^2-(9x-4)=0

We add all the numbers together, and all the variables

-1x^2-(9x-4)+45=0

We get rid of parentheses

-1x^2-9x+4+45=0

We add all the numbers together, and all the variables

-1x^2-9x+49=0

a = -1; b = -9; c = +49;
Δ = b2-4ac
Δ = -92-4·(-1)·49
Δ = 277
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{277}}{2*-1}=\frac{9-\sqrt{277}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{277}}{2*-1}=\frac{9+\sqrt{277}}{-2}
$