(3x-6)(14x+21)=0

Solution for (3x-6)(14x+21)=0 equation:

(3x-6)(14x+21)=0

We multiply parentheses ..

(+42x^2+63x-84x-126)=0

We get rid of parentheses

42x^2+63x-84x-126=0

We add all the numbers together, and all the variables

42x^2-21x-126=0

a = 42; b = -21; c = -126;
Δ = b2-4ac
Δ = -212-4·42·(-126)
Δ = 21609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21609}=147$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-147}{2*42}=\frac{-126}{84}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+147}{2*42}=\frac{168}{84}
=2
$