(x-3)(7x+2)=0

Solution for (x-3)(7x+2)=0 equation:

(x-3)(7x+2)=0

We multiply parentheses ..

(+7x^2+2x-21x-6)=0

We get rid of parentheses

7x^2+2x-21x-6=0

We add all the numbers together, and all the variables

7x^2-19x-6=0

a = 7; b = -19; c = -6;
Δ = b2-4ac
Δ = -192-4·7·(-6)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-23}{2*7}=\frac{-4}{14}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+23}{2*7}=\frac{42}{14}
=3
$