32x=2x^2

Solution for 32x=2x^2 equation:

32x=2x^2

We move all terms to the left:

32x-(2x^2)=0

determiningTheFunctionDomain
-2x^2+32x=0

a = -2; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-2)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-2}=\frac{-64}{-4}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-2}=\frac{0}{-4}
=0
$