4x^2+32x=-48

Solution for 4x^2+32x=-48 equation:

4x^2+32x=-48

We move all terms to the left:

4x^2+32x-(-48)=0

We add all the numbers together, and all the variables

4x^2+32x+48=0

a = 4; b = 32; c = +48;
Δ = b2-4ac
Δ = 322-4·4·48
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-16}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+16}{2*4}=\frac{-16}{8}
=-2
$