4x(x+7)+48=0

Solution for 4x(x+7)+48=0 equation:

4x(x+7)+48=0

We multiply parentheses

4x^2+28x+48=0

a = 4; b = 28; c = +48;
Δ = b2-4ac
Δ = 282-4·4·48
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4}{2*4}=\frac{-32}{8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4}{2*4}=\frac{-24}{8}
=-3
$