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

Solution for 0=(3x-1)(x+6) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+3x^2+18x-1x-6)), so:

(+3x^2+18x-1x-6)

We get rid of parentheses

3x^2+18x-1x-6

We add all the numbers together, and all the variables

3x^2+17x-6

Back to the equation:

-(3x^2+17x-6)


We get rid of parentheses

-3x^2-17x+6=0

a = -3; b = -17; c = +6;
Δ = b2-4ac
Δ = -172-4·(-3)·6
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-19}{2*-3}=\frac{-2}{-6}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+19}{2*-3}=\frac{36}{-6}
=-6
$