41=-16x^2+50x+6

Solution for 41=-16x^2+50x+6 equation:

41=-16x^2+50x+6

We move all terms to the left:

41-(-16x^2+50x+6)=0

We get rid of parentheses

16x^2-50x-6+41=0

We add all the numbers together, and all the variables

16x^2-50x+35=0

a = 16; b = -50; c = +35;
Δ = b2-4ac
Δ = -502-4·16·35
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{65}}{2*16}=\frac{50-2\sqrt{65}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{65}}{2*16}=\frac{50+2\sqrt{65}}{32}
$