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

Solution for 6(x-3)(x+7)=0 equation:

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

We multiply parentheses ..

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

We multiply parentheses

6x^2+42x-18x-126=0

We add all the numbers together, and all the variables

6x^2+24x-126=0

a = 6; b = 24; c = -126;
Δ = b2-4ac
Δ = 242-4·6·(-126)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-60}{2*6}=\frac{-84}{12}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+60}{2*6}=\frac{36}{12}
=3
$