3x-x^2=9-x-56

Solution for 3x-x^2=9-x-56 equation:

3x-x^2=9-x-56

We move all terms to the left:

3x-x^2-(9-x-56)=0

We add all the numbers together, and all the variables

-x^2+3x-(-1x-47)=0

We add all the numbers together, and all the variables

-1x^2+3x-(-1x-47)=0

We get rid of parentheses

-1x^2+3x+1x+47=0

We add all the numbers together, and all the variables

-1x^2+4x+47=0

a = -1; b = 4; c = +47;
Δ = b2-4ac
Δ = 42-4·(-1)·47
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{51}}{2*-1}=\frac{-4-2\sqrt{51}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{51}}{2*-1}=\frac{-4+2\sqrt{51}}{-2}
$