32x^2=-16x

Solution for 32x^2=-16x equation:

32x^2=-16x

We move all terms to the left:

32x^2-(-16x)=0

We get rid of parentheses

32x^2+16x=0

a = 32; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·32·0
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{-(16)-16}{2*32}=\frac{-32}{64}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*32}=\frac{0}{64}
=0
$