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

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

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

We multiply parentheses ..

3(+2x^2-14x+3x-21)=0

We multiply parentheses

6x^2-42x+9x-63=0

We add all the numbers together, and all the variables

6x^2-33x-63=0

a = 6; b = -33; c = -63;
Δ = b2-4ac
Δ = -332-4·6·(-63)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-51}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+51}{2*6}=\frac{84}{12}
=7
$