(7x+2)(-3x+1)=0

Solution for (7x+2)(-3x+1)=0 equation:

(7x+2)(-3x+1)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-21x^2+x+2=0

a = -21; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-21)·2
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*-21}=\frac{-14}{-42}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*-21}=\frac{12}{-42}
=-2/7
$