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

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

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

We multiply parentheses

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

We multiply parentheses ..

-7x^2+(+14x^2+7x+6x+3)-3x=0

We get rid of parentheses

-7x^2+14x^2+7x+6x-3x+3=0

We add all the numbers together, and all the variables

7x^2+10x+3=0

a = 7; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·7·3
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*7}=\frac{-14}{14}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*7}=\frac{-6}{14}
=-3/7
$