(X+3)(6X+1)=o

Solution for (X+3)(6X+1)=o equation:

(X+3)(6X+1)=X

We move all terms to the left:

(X+3)(6X+1)-(X)=0

We add all the numbers together, and all the variables

-1X+(X+3)(6X+1)=0

We multiply parentheses ..

(+6X^2+X+18X+3)-1X=0

We get rid of parentheses

6X^2+X+18X-1X+3=0

We add all the numbers together, and all the variables

6X^2+18X+3=0

a = 6; b = 18; c = +3;
Δ = b2-4ac
Δ = 182-4·6·3
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{7}}{2*6}=\frac{-18-6\sqrt{7}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{7}}{2*6}=\frac{-18+6\sqrt{7}}{12}
$