32.5=-0.01x^2+0.975x+16

Solution for 32.5=-0.01x^2+0.975x+16 equation:

32.5=-0.01x^2+0.975x+16

We move all terms to the left:

32.5-(-0.01x^2+0.975x+16)=0

We get rid of parentheses

0.01x^2-0.975x-16+32.5=0

We add all the numbers together, and all the variables

0.01x^2-0.975x+16.5=0

a = 0.01; b = -0.975; c = +16.5;
Δ = b2-4ac
Δ = -0.9752-4·0.01·16.5
Δ = 0.290625
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{-(-0.975)-\sqrt{0.290625}}{2*0.01}=\frac{0.975-\sqrt{0.290625}}{0.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.975)+\sqrt{0.290625}}{2*0.01}=\frac{0.975+\sqrt{0.290625}}{0.02}
$