X(x+2)+(x+1)=54

Solution for X(x+2)+(x+1)=54 equation:

X(X+2)+(X+1)=54

We move all terms to the left:

X(X+2)+(X+1)-(54)=0

We multiply parentheses

X^2+2X+(X+1)-54=0

We get rid of parentheses

X^2+2X+X+1-54=0

We add all the numbers together, and all the variables

X^2+3X-53=0

a = 1; b = 3; c = -53;
Δ = b2-4ac
Δ = 32-4·1·(-53)
Δ = 221
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{-(3)-\sqrt{221}}{2*1}=\frac{-3-\sqrt{221}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{221}}{2*1}=\frac{-3+\sqrt{221}}{2}
$