X+(x+1)+(x+2)(x+3)=756

Solution for X+(x+1)+(x+2)(x+3)=756 equation:

X+(X+1)+(X+2)(X+3)=756

We move all terms to the left:

X+(X+1)+(X+2)(X+3)-(756)=0

We get rid of parentheses

X+X+(X+2)(X+3)+1-756=0

We multiply parentheses ..

(+X^2+3X+2X+6)+X+X+1-756=0

We add all the numbers together, and all the variables

(+X^2+3X+2X+6)+2X-755=0

We get rid of parentheses

X^2+3X+2X+2X+6-755=0

We add all the numbers together, and all the variables

X^2+7X-749=0

a = 1; b = 7; c = -749;
Δ = b2-4ac
Δ = 72-4·1·(-749)
Δ = 3045
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{-(7)-\sqrt{3045}}{2*1}=\frac{-7-\sqrt{3045}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{3045}}{2*1}=\frac{-7+\sqrt{3045}}{2}
$