32=-16x^2+35x+20

Solution for 32=-16x^2+35x+20 equation:

32=-16x^2+35x+20

We move all terms to the left:

32-(-16x^2+35x+20)=0

We get rid of parentheses

16x^2-35x-20+32=0

We add all the numbers together, and all the variables

16x^2-35x+12=0

a = 16; b = -35; c = +12;
Δ = b2-4ac
Δ = -352-4·16·12
Δ = 457
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{-(-35)-\sqrt{457}}{2*16}=\frac{35-\sqrt{457}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{457}}{2*16}=\frac{35+\sqrt{457}}{32}
$