X(x+6)+3(x+6)=149

Solution for X(x+6)+3(x+6)=149 equation:

X(X+6)+3(X+6)=149

We move all terms to the left:

X(X+6)+3(X+6)-(149)=0

We multiply parentheses

X^2+6X+3X+18-149=0

We add all the numbers together, and all the variables

X^2+9X-131=0

a = 1; b = 9; c = -131;
Δ = b2-4ac
Δ = 92-4·1·(-131)
Δ = 605
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:

$\sqrt{\Delta}=\sqrt{605}=\sqrt{121*5}=\sqrt{121}*\sqrt{5}=11\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-11\sqrt{5}}{2*1}=\frac{-9-11\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11\sqrt{5}}{2*1}=\frac{-9+11\sqrt{5}}{2}
$