12w^2+32w=-5

Solution for 12w^2+32w=-5 equation:

12w^2+32w=-5

We move all terms to the left:

12w^2+32w-(-5)=0

We add all the numbers together, and all the variables

12w^2+32w+5=0

a = 12; b = 32; c = +5;
Δ = b2-4ac
Δ = 322-4·12·5
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-28}{2*12}=\frac{-60}{24}
=-2+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+28}{2*12}=\frac{-4}{24}
=-1/6
$