71=125x-16x^2

Solution for 71=125x-16x^2 equation:

71=125x-16x^2

We move all terms to the left:

71-(125x-16x^2)=0

We get rid of parentheses

16x^2-125x+71=0

a = 16; b = -125; c = +71;
Δ = b2-4ac
Δ = -1252-4·16·71
Δ = 11081
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{-(-125)-\sqrt{11081}}{2*16}=\frac{125-\sqrt{11081}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125)+\sqrt{11081}}{2*16}=\frac{125+\sqrt{11081}}{32}
$