x+3=55-x^2

Solution for x+3=55-x^2 equation:

x+3=55-x^2

We move all terms to the left:

x+3-(55-x^2)=0

We get rid of parentheses

x^2+x-55+3=0

We add all the numbers together, and all the variables

x^2+x-52=0

a = 1; b = 1; c = -52;
Δ = b2-4ac
Δ = 12-4·1·(-52)
Δ = 209
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{-(1)-\sqrt{209}}{2*1}=\frac{-1-\sqrt{209}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{209}}{2*1}=\frac{-1+\sqrt{209}}{2}
$