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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6X^2-17X-3=0

a = 6; b = -17; c = -3;
Δ = b2-4ac
Δ = -172-4·6·(-3)
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*6}=\frac{-2}{12}
=-1/6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+19}{2*6}=\frac{36}{12}
=3
$