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

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

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

We multiply parentheses

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

We add all the numbers together, and all the variables

-4x^2-11x=0

a = -4; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-4)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-4}=\frac{22}{-8}
=-2+3/4
$