X(x+6)+x=18

Solution for X(x+6)+x=18 equation:

X(X+6)+X=18

We move all terms to the left:

X(X+6)+X-(18)=0

We add all the numbers together, and all the variables

X+X(X+6)-18=0

We multiply parentheses

X^2+X+6X-18=0

We add all the numbers together, and all the variables

X^2+7X-18=0

a = 1; b = 7; c = -18;
Δ = b2-4ac
Δ = 72-4·1·(-18)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*1}=\frac{-18}{2}
=-9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*1}=\frac{4}{2}
=2
$