2x+x^2=54

Solution for 2x+x^2=54 equation:

2x+x^2=54

We move all terms to the left:

2x+x^2-(54)=0

a = 1; b = 2; c = -54;
Δ = b2-4ac
Δ = 22-4·1·(-54)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{55}}{2*1}=\frac{-2-2\sqrt{55}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{55}}{2*1}=\frac{-2+2\sqrt{55}}{2}
$