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