(3x-14)(7x+12)=0

Solution for (3x-14)(7x+12)=0 equation:

(3x-14)(7x+12)=0

We multiply parentheses ..

(+21x^2+36x-98x-168)=0

We get rid of parentheses

21x^2+36x-98x-168=0

We add all the numbers together, and all the variables

21x^2-62x-168=0

a = 21; b = -62; c = -168;
Δ = b2-4ac
Δ = -622-4·21·(-168)
Δ = 17956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17956}=134$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-134}{2*21}=\frac{-72}{42}
=-1+5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+134}{2*21}=\frac{196}{42}
=4+2/3
$