(4x+14)(x+8)=0

Solution for (4x+14)(x+8)=0 equation:

(4x+14)(x+8)=0

We multiply parentheses ..

(+4x^2+32x+14x+112)=0

We get rid of parentheses

4x^2+32x+14x+112=0

We add all the numbers together, and all the variables

4x^2+46x+112=0

a = 4; b = 46; c = +112;
Δ = b2-4ac
Δ = 462-4·4·112
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-18}{2*4}=\frac{-64}{8}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+18}{2*4}=\frac{-28}{8}
=-3+1/2
$