(6x+1)(3x-7)=0

Solution for (6x+1)(3x-7)=0 equation:

(6x+1)(3x-7)=0

We multiply parentheses ..

(+18x^2-42x+3x-7)=0

We get rid of parentheses

18x^2-42x+3x-7=0

We add all the numbers together, and all the variables

18x^2-39x-7=0

a = 18; b = -39; c = -7;
Δ = b2-4ac
Δ = -392-4·18·(-7)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-45}{2*18}=\frac{-6}{36}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+45}{2*18}=\frac{84}{36}
=2+1/3
$