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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

7x^2+39x-18=0

a = 7; b = 39; c = -18;
Δ = b2-4ac
Δ = 392-4·7·(-18)
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*7}=\frac{-84}{14}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+45}{2*7}=\frac{6}{14}
=3/7
$