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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

3x^2-18x+x-6=0

We add all the numbers together, and all the variables

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
$