-7(2x+3)(x-12)=0

Solution for -7(2x+3)(x-12)=0 equation:

-7(2x+3)(x-12)=0

We multiply parentheses ..

-7(+2x^2-24x+3x-36)=0

We multiply parentheses

-14x^2+168x-21x+252=0

We add all the numbers together, and all the variables

-14x^2+147x+252=0

a = -14; b = 147; c = +252;
Δ = b2-4ac
Δ = 1472-4·(-14)·252
Δ = 35721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35721}=189$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(147)-189}{2*-14}=\frac{-336}{-28}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(147)+189}{2*-14}=\frac{42}{-28}
=-1+1/2
$