X+(x+1)(x+2)=45

Solution for X+(x+1)(x+2)=45 equation:

X+(X+1)(X+2)=45

We move all terms to the left:

X+(X+1)(X+2)-(45)=0

We multiply parentheses ..

(+X^2+2X+X+2)+X-45=0

We get rid of parentheses

X^2+2X+X+X+2-45=0

We add all the numbers together, and all the variables

X^2+4X-43=0

a = 1; b = 4; c = -43;
Δ = b2-4ac
Δ = 42-4·1·(-43)
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{47}}{2*1}=\frac{-4-2\sqrt{47}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{47}}{2*1}=\frac{-4+2\sqrt{47}}{2}
$