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

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

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

We multiply parentheses ..

(+3x^2+7x+12x+28)=0

We get rid of parentheses

3x^2+7x+12x+28=0

We add all the numbers together, and all the variables

3x^2+19x+28=0

a = 3; b = 19; c = +28;
Δ = b2-4ac
Δ = 192-4·3·28
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-5}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+5}{2*3}=\frac{-14}{6}
=-2+1/3
$