32=-16x^2+50x+5

Solution for 32=-16x^2+50x+5 equation:

32=-16x^2+50x+5

We move all terms to the left:

32-(-16x^2+50x+5)=0

We get rid of parentheses

16x^2-50x-5+32=0

We add all the numbers together, and all the variables

16x^2-50x+27=0

a = 16; b = -50; c = +27;
Δ = b2-4ac
Δ = -502-4·16·27
Δ = 772
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{193}}{2*16}=\frac{50-2\sqrt{193}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{193}}{2*16}=\frac{50+2\sqrt{193}}{32}
$