(3x+7)(-4x-6)=0

Solution for (3x+7)(-4x-6)=0 equation:

(3x+7)(-4x-6)=0

We multiply parentheses ..

(-12x^2-18x-28x-42)=0

We get rid of parentheses

-12x^2-18x-28x-42=0

We add all the numbers together, and all the variables

-12x^2-46x-42=0

a = -12; b = -46; c = -42;
Δ = b2-4ac
Δ = -462-4·(-12)·(-42)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-10}{2*-12}=\frac{36}{-24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+10}{2*-12}=\frac{56}{-24}
=-2+1/3
$