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

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

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

We multiply parentheses ..

(-6x^2-24x+21x+84)=0

We get rid of parentheses

-6x^2-24x+21x+84=0

We add all the numbers together, and all the variables

-6x^2-3x+84=0

a = -6; b = -3; c = +84;
Δ = b2-4ac
Δ = -32-4·(-6)·84
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-45}{2*-6}=\frac{-42}{-12}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+45}{2*-6}=\frac{48}{-12}
=-4
$