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

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

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

We multiply parentheses

-7x^2-21x-3x-12=0

We add all the numbers together, and all the variables

-7x^2-24x-12=0

a = -7; b = -24; c = -12;
Δ = b2-4ac
Δ = -242-4·(-7)·(-12)
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{15}}{2*-7}=\frac{24-4\sqrt{15}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{15}}{2*-7}=\frac{24+4\sqrt{15}}{-14}
$