(X+6)(2x+1)=6

Solution for (X+6)(2x+1)=6 equation:

(X+6)(2X+1)=6

We move all terms to the left:

(X+6)(2X+1)-(6)=0

We multiply parentheses ..

(+2X^2+X+12X+6)-6=0

We get rid of parentheses

2X^2+X+12X+6-6=0

We add all the numbers together, and all the variables

2X^2+13X=0

a = 2; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·2·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*2}=\frac{-26}{4}
=-6+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*2}=\frac{0}{4}
=0
$