80x-3x^2-125+16x=0

Solution for 80x-3x^2-125+16x=0 equation:

80x-3x^2-125+16x=0

We add all the numbers together, and all the variables

-3x^2+96x-125=0

a = -3; b = 96; c = -125;
Δ = b2-4ac
Δ = 962-4·(-3)·(-125)
Δ = 7716
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:

$\sqrt{\Delta}=\sqrt{7716}=\sqrt{4*1929}=\sqrt{4}*\sqrt{1929}=2\sqrt{1929}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-2\sqrt{1929}}{2*-3}=\frac{-96-2\sqrt{1929}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+2\sqrt{1929}}{2*-3}=\frac{-96+2\sqrt{1929}}{-6}
$