2x+56-x^2=30

Solution for 2x+56-x^2=30 equation:

2x+56-x^2=30

We move all terms to the left:

2x+56-x^2-(30)=0

We add all the numbers together, and all the variables

-1x^2+2x+26=0

a = -1; b = 2; c = +26;
Δ = b2-4ac
Δ = 22-4·(-1)·26
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{3}}{2*-1}=\frac{-2-6\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{3}}{2*-1}=\frac{-2+6\sqrt{3}}{-2}
$