X(x+1)+(x+2)(x+3)=26

Solution for X(x+1)+(x+2)(x+3)=26 equation:

X(X+1)+(X+2)(X+3)=26

We move all terms to the left:

X(X+1)+(X+2)(X+3)-(26)=0

We multiply parentheses

X^2+X+(X+2)(X+3)-26=0

We multiply parentheses ..

X^2+(+X^2+3X+2X+6)+X-26=0

We get rid of parentheses

X^2+X^2+3X+2X+X+6-26=0

We add all the numbers together, and all the variables

2X^2+6X-20=0

a = 2; b = 6; c = -20;
Δ = b2-4ac
Δ = 62-4·2·(-20)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*2}=\frac{-20}{4}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*2}=\frac{8}{4}
=2
$