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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-3x^2+21x-1x+7)=0

We get rid of parentheses

-3x^2+21x-1x+7=0

We add all the numbers together, and all the variables

-3x^2+20x+7=0

a = -3; b = 20; c = +7;
Δ = b2-4ac
Δ = 202-4·(-3)·7
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-22}{2*-3}=\frac{-42}{-6}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+22}{2*-3}=\frac{2}{-6}
=-1/3
$