32.5=0.01x^2+0.0975-16.5

Solution for 32.5=0.01x^2+0.0975-16.5 equation:

32.5=0.01x^2+0.0975-16.5

We move all terms to the left:

32.5-(0.01x^2+0.0975-16.5)=0

We get rid of parentheses

-0.01x^2-0.0975+16.5+32.5=0

We add all the numbers together, and all the variables

-0.01x^2+48.9025=0

a = -0.01; b = 0; c = +48.9025;
Δ = b2-4ac
Δ = 02-4·(-0.01)·48.9025
Δ = 1.9561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{1.9561}}{2*-0.01}=\frac{0-\sqrt{1.9561}}{-0.02}
=-\frac{\sqrt{}}{-0.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{1.9561}}{2*-0.01}=\frac{0+\sqrt{1.9561}}{-0.02}
=\frac{\sqrt{}}{-0.02}
$