4(x^2+6)+28x=0

Solution for 4(x^2+6)+28x=0 equation:

4(x^2+6)+28x=0

We add all the numbers together, and all the variables

28x+4(x^2+6)=0

We multiply parentheses

4x^2+28x+24=0

a = 4; b = 28; c = +24;
Δ = b2-4ac
Δ = 282-4·4·24
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-20}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+20}{2*4}=\frac{-8}{8}
=-1
$